Animate a pendulum
You are encouraged to solve this task according to the task description, using any language you may know.
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a simple gravity pendulum.
- Task
Create a simple physical model of a pendulum and animate it.
Ada
This does not use a GUI, it simply animates the pendulum and prints out the positions. If you want, you can replace the output method with graphical update methods.
X and Y are relative positions of the pendulum to the anchor.
pendulums.ads: <lang Ada>generic
type Float_Type is digits <>; Gravitation : Float_Type;
package Pendulums is
type Pendulum is private;
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum;
function Get_X (From : Pendulum) return Float_Type;
function Get_Y (From : Pendulum) return Float_Type;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration);
private
type Pendulum is record
Length : Float_Type;
Theta : Float_Type;
X : Float_Type;
Y : Float_Type;
Velocity : Float_Type;
end record;
end Pendulums;</lang>
pendulums.adb: <lang Ada>with Ada.Numerics.Generic_Elementary_Functions; package body Pendulums is
package Math is new Ada.Numerics.Generic_Elementary_Functions (Float_Type);
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum is
Result : Pendulum;
begin
Result.Length := Length;
Result.Theta := Theta0 / 180.0 * Ada.Numerics.Pi;
Result.X := Math.Sin (Theta0) * Length;
Result.Y := Math.Cos (Theta0) * Length;
Result.Velocity := 0.0;
return Result;
end New_Pendulum;
function Get_X (From : Pendulum) return Float_Type is
begin
return From.X;
end Get_X;
function Get_Y (From : Pendulum) return Float_Type is
begin
return From.Y;
end Get_Y;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration) is
Acceleration : constant Float_Type := Gravitation / Item.Length *
Math.Sin (Item.Theta);
begin
Item.X := Math.Sin (Item.Theta) * Item.Length;
Item.Y := Math.Cos (Item.Theta) * Item.Length;
Item.Velocity := Item.Velocity +
Acceleration * Float_Type (Time);
Item.Theta := Item.Theta +
Item.Velocity * Float_Type (Time);
end Update_Pendulum;
end Pendulums;</lang>
example main.adb: <lang Ada>with Ada.Text_IO; with Ada.Calendar; with Pendulums;
procedure Main is
package Float_Pendulum is new Pendulums (Float, -9.81); use Float_Pendulum; use type Ada.Calendar.Time;
My_Pendulum : Pendulum := New_Pendulum (10.0, 30.0); Now, Before : Ada.Calendar.Time;
begin
Before := Ada.Calendar.Clock;
loop
Delay 0.1;
Now := Ada.Calendar.Clock;
Update_Pendulum (My_Pendulum, Now - Before);
Before := Now;
-- output positions relative to origin
-- replace with graphical output if wanted
Ada.Text_IO.Put_Line (" X: " & Float'Image (Get_X (My_Pendulum)) &
" Y: " & Float'Image (Get_Y (My_Pendulum)));
end loop;
end Main;</lang>
- Output:
X: 5.00000E+00 Y: 8.66025E+00 X: 4.95729E+00 Y: 8.68477E+00 X: 4.87194E+00 Y: 8.73294E+00 X: 4.74396E+00 Y: 8.80312E+00 X: 4.57352E+00 Y: 8.89286E+00 X: 4.36058E+00 Y: 8.99919E+00 X: 4.10657E+00 Y: 9.11790E+00 X: 3.81188E+00 Y: 9.24498E+00 X: 3.47819E+00 Y: 9.37562E+00 X: 3.10714E+00 Y: 9.50504E+00 X: 2.70211E+00 Y: 9.62801E+00 X: 2.26635E+00 Y: 9.73980E+00 X: 1.80411E+00 Y: 9.83591E+00 X: 1.32020E+00 Y: 9.91247E+00 X: 8.20224E-01 Y: 9.96630E+00 X: 3.10107E-01 Y: 9.99519E+00 X: -2.03865E-01 Y: 9.99792E+00 X: -7.15348E-01 Y: 9.97438E+00 X: -1.21816E+00 Y: 9.92553E+00 X: -1.70581E+00 Y: 9.85344E+00 X: -2.17295E+00 Y: 9.76106E+00 X: -2.61452E+00 Y: 9.65216E+00 X: -3.02618E+00 Y: 9.53112E+00 X: -3.40427E+00 Y: 9.40271E+00 X: -3.74591E+00 Y: 9.27190E+00 X: -4.04873E+00 Y: 9.14373E+00 X: -4.31141E+00 Y: 9.02285E+00 X: -4.53271E+00 Y: 8.91373E+00 X: -4.71186E+00 Y: 8.82034E+00 X: -4.84868E+00 Y: 8.74587E+00 X: -4.94297E+00 Y: 8.69293E+00 X: -4.99459E+00 Y: 8.66337E+00 X: -5.00352E+00 Y: 8.65822E+00 ...
AutoHotkey
This version doesn't use an complex physics calculation - I found a faster way.
<lang AutoHotkey>SetBatchlines,-1
- settings
SizeGUI:={w:650,h:400} ;Guisize pendulum:={length:300,maxangle:90,speed:2,size:30,center:{x:Sizegui.w//2,y:10}} ;pendulum length, size, center, speed and maxangle
pendulum.maxangle:=pendulum.maxangle*0.01745329252 p_Token:=Gdip_Startup() Gui,+LastFound Gui,show,% "w" SizeGUI.w " h" SizeGUI.h hwnd:=WinActive() hdc:=GetDC(hwnd) start:=A_TickCount/1000 G:=Gdip_GraphicsFromHDC(hdc) pBitmap:=Gdip_CreateBitmap(650, 450) G2:=Gdip_GraphicsFromImage(pBitmap) Gdip_SetSmoothingMode(G2, 4) pBrush := Gdip_BrushCreateSolid(0xff0000FF) pBrush2 := Gdip_BrushCreateSolid(0xFF777700) pPen:=Gdip_CreatePenFromBrush(pBrush2, 10) SetTimer,Update,10
Update: Gdip_GraphicsClear(G2,0xFFFFFFFF) time:=start-(A_TickCount/1000*pendulum.speed) angle:=sin(time)*pendulum.maxangle x2:=sin(angle)*pendulum.length+pendulum.center.x y2:=cos(angle)*pendulum.length+pendulum.center.y Gdip_DrawLine(G2,pPen,pendulum.center.x,pendulum.center.y,x2,y2) GDIP_DrawCircle(G2,pBrush,pendulum.center.x,pendulum.center.y,15) GDIP_DrawCircle(G2,pBrush2,x2,y2,pendulum.size) Gdip_DrawImage(G, pBitmap) return
GDIP_DrawCircle(g,b,x,y,r){ Gdip_FillEllipse(g, b, x-r//2,y-r//2 , r, r) }
GuiClose: ExitApp</lang>
BASIC
BBC BASIC
<lang bbcbasic> MODE 8
*FLOAT 64
VDU 23,23,4;0;0;0; : REM Set line thickness
theta = RAD(40) : REM initial displacement
g = 9.81 : REM acceleration due to gravity
l = 0.50 : REM length of pendulum in metres
REPEAT
PROCpendulum(theta, l)
WAIT 1
PROCpendulum(theta, l)
accel = - g * SIN(theta) / l / 100
speed += accel / 100
theta += speed
UNTIL FALSE
END
DEF PROCpendulum(a, l)
LOCAL pivotX, pivotY, bobX, bobY
pivotX = 640
pivotY = 800
bobX = pivotX + l * 1000 * SIN(a)
bobY = pivotY - l * 1000 * COS(a)
GCOL 3,6
LINE pivotX, pivotY, bobX, bobY
GCOL 3,11
CIRCLE FILL bobX + 24 * SIN(a), bobY - 24 * COS(a), 24
ENDPROC</lang>
Commodore BASIC
<lang commodorebasic>10 GOSUB 1000 20 THETA = π/2 30 G = 9.81 40 L = 0.5 50 SPEED = 0 60 PX = 20 70 PY = 1 80 BX = PX+L*20*SIN(THETA) 90 BY = PY-L*20*COS(THETA) 100 PRINT CHR$(147); 110 FOR X=PX TO BX STEP (BX-PX)/10 120 Y=PY+(X-PX)*(BY-PY)/(BX-PX) 130 PRINT CHR$(19);LEFT$(X$,X);LEFT$(Y$,Y);"." 140 NEXT 150 PRINT CHR$(19);LEFT$(X$,BX);LEFT$(Y$,BY);CHR$(113) 160 ACCEL=G*SIN(THETA)/L/50 170 SPEED=SPEED+ACCEL/10 180 THETA=THETA+SPEED 190 GOTO 80 980 REM ** SETUP STRINGS TO BE USED ** 990 REM ** FOR CURSOR POSITIONING ** 1000 FOR I=0 TO 39: X$ = X$+CHR$(29): NEXT 1010 FOR I=0 TO 24: Y$ = Y$+CHR$(17): NEXT 1020 RETURN</lang>
FreeBASIC
<lang freebasic>Const PI = 3.141592920 Dim As Double theta, g, l, accel, speed, px, py, bx, by theta = PI/2 g = 9.81 l = 1 speed = 0 px = 320 py = 10 Screen 17 '640x400 graphic Do
bx=px+l*300*Sin(theta) by=py-l*300*Cos(theta) Cls Line (px,py)-(bx,by) Circle (bx,by),5,,,,,F accel=g*Sin(theta)/l/100 speed=speed+accel/100 theta=theta+speed Draw String (0,370), "Pendulum" Draw String (0,385), "Press any key to quit" Sleep 10
Loop Until Inkey()<>""</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Pendulum.bas" 110 LET THETA=RAD(50):LET G=9.81:LET L=.5 120 CALL INIC 130 CALL DRAWING 140 CALL ANIMATE 150 CALL RESET 160 END 170 DEF INIC 180 CLOSE #102 190 OPTION ANGLE RADIANS 200 SET STATUS OFF:SET INTERRUPT STOP OFF:SET BORDER 56 210 SET VIDEO MODE 1:SET VIDEO COLOR 1:SET VIDEO X 14:SET VIDEO Y 8 220 FOR I=1 TO 24 230 OPEN #I:"video:" 240 SET #I:PALETTE 56,0,255,YELLOW 250 NEXT 260 END DEF 270 DEF DRAWING 280 LET SPD=0 290 FOR I=1 TO 24 300 DISPLAY #I:AT 3 FROM 1 TO 8 310 SET #I:INK 2 320 PLOT #I:224,280,ELLIPSE 10,10 330 PLOT #I:0,280;214,280,234,280;446,280 340 SET #I:INK 1 350 CALL PENDULUM(THETA,L,I) 360 LET ACC=-G*SIN(THETA)/L/100 370 LET SPD=SPD+ACC/10.5 380 LET THETA=THETA+SPD 390 NEXT 400 END DEF 410 DEF PENDULUM(A,L,CH) 420 LET PX=224:LET PY=280 430 LET BX=PX+L*460*SIN(A) 440 LET BY=PY-L*460*COS(A) 450 PLOT #CH:PX,PY;BX,BY 460 PLOT #CH:BX+24*SIN(A),BY-24*COS(A),ELLIPSE 20,20, 470 SET #CH:INK 3:PLOT #CH:PAINT 480 END DEF 490 DEF ANIMATE 500 DO 510 FOR I=1 TO 24 520 DISPLAY #I:AT 3 FROM 1 TO 8 530 NEXT 540 FOR I=23 TO 2 STEP-1 550 DISPLAY #I:AT 3 FROM 1 TO 8 560 NEXT 570 LOOP UNTIL INKEY$=CHR$(27) 580 END DEF 590 DEF RESET 600 TEXT 40:SET STATUS ON:SET INTERRUPT STOP ON:SET BORDER 0 610 FOR I=24 TO 1 STEP-1 620 CLOSE #I 630 NEXT 640 END DEF</lang>
C
<lang c>#include <stdlib.h>
- include <math.h>
- include <GL/glut.h>
- include <GL/gl.h>
- include <sys/time.h>
- define length 5
- define g 9.8
double alpha, accl, omega = 0, E; struct timeval tv;
double elappsed() { struct timeval now; gettimeofday(&now, 0); int ret = (now.tv_sec - tv.tv_sec) * 1000000 + now.tv_usec - tv.tv_usec; tv = now; return ret / 1.e6; }
void resize(int w, int h) { glViewport(0, 0, w, h); glMatrixMode(GL_PROJECTION); glLoadIdentity();
glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glOrtho(0, w, h, 0, -1, 1); }
void render() { double x = 320 + 300 * sin(alpha), y = 300 * cos(alpha); resize(640, 320);
glClear(GL_COLOR_BUFFER_BIT);
glBegin(GL_LINES); glVertex2d(320, 0); glVertex2d(x, y); glEnd(); glFlush();
double us = elappsed(); alpha += (omega + us * accl / 2) * us; omega += accl * us;
/* don't let precision error go out of hand */ if (length * g * (1 - cos(alpha)) >= E) { alpha = (alpha < 0 ? -1 : 1) * acos(1 - E / length / g); omega = 0; } accl = -g / length * sin(alpha); }
void init_gfx(int *c, char **v) { glutInit(c, v); glutInitDisplayMode(GLUT_RGB); glutInitWindowSize(640, 320); glutIdleFunc(render); glutCreateWindow("Pendulum"); }
int main(int c, char **v) { alpha = 4 * atan2(1, 1) / 2.1; E = length * g * (1 - cos(alpha));
accl = -g / length * sin(alpha); omega = 0;
gettimeofday(&tv, 0); init_gfx(&c, v); glutMainLoop(); return 0; }</lang>
C#
<lang csharp> using System; using System.Drawing; using System.Windows.Forms;
class CSharpPendulum {
Form _form;
Timer _timer;
double _angle = Math.PI / 2,
_angleAccel,
_angleVelocity = 0,
_dt = 0.1;
int _length = 50;
[STAThread]
static void Main()
{
var p = new CSharpPendulum();
}
public CSharpPendulum()
{
_form = new Form() { Text = "Pendulum", Width = 200, Height = 200 };
_timer = new Timer() { Interval = 30 };
_timer.Tick += delegate(object sender, EventArgs e)
{
int anchorX = (_form.Width / 2) - 12,
anchorY = _form.Height / 4,
ballX = anchorX + (int)(Math.Sin(_angle) * _length),
ballY = anchorY + (int)(Math.Cos(_angle) * _length);
_angleAccel = -9.81 / _length * Math.Sin(_angle);
_angleVelocity += _angleAccel * _dt;
_angle += _angleVelocity * _dt;
Bitmap dblBuffer = new Bitmap(_form.Width, _form.Height);
Graphics g = Graphics.FromImage(dblBuffer);
Graphics f = Graphics.FromHwnd(_form.Handle);
g.DrawLine(Pens.Black, new Point(anchorX, anchorY), new Point(ballX, ballY));
g.FillEllipse(Brushes.Black, anchorX - 3, anchorY - 4, 7, 7);
g.FillEllipse(Brushes.DarkGoldenrod, ballX - 7, ballY - 7, 14, 14);
f.Clear(Color.White);
f.DrawImage(dblBuffer, new Point(0, 0));
};
_timer.Start();
Application.Run(_form);
}
} </lang>
C++
File wxPendulumDlg.hpp <lang cpp>
- ifndef __wxPendulumDlg_h__
- define __wxPendulumDlg_h__
// --------------------- /// @author Martin Ettl /// @date 2013-02-03 // ---------------------
- ifdef __BORLANDC__
- pragma hdrstop
- endif
- ifndef WX_PRECOMP
- include <wx/wx.h>
- include <wx/dialog.h>
- else
- include <wx/wxprec.h>
- endif
- include <wx/timer.h>
- include <wx/dcbuffer.h>
- include <cmath>
class wxPendulumDlgApp : public wxApp {
public:
bool OnInit();
int OnExit();
};
class wxPendulumDlg : public wxDialog {
public:
wxPendulumDlg(wxWindow *parent, wxWindowID id = 1, const wxString &title = wxT("wxPendulum"),
const wxPoint& pos = wxDefaultPosition, const wxSize& size = wxDefaultSize, long style = wxSUNKEN_BORDER | wxCAPTION | wxRESIZE_BORDER | wxSYSTEM_MENU | wxDIALOG_NO_PARENT | wxMINIMIZE_BOX | wxMAXIMIZE_BOX | wxCLOSE_BOX);
virtual ~wxPendulumDlg();
// Event handler
void wxPendulumDlgPaint(wxPaintEvent& event);
void wxPendulumDlgSize(wxSizeEvent& event);
void OnTimer(wxTimerEvent& event);
private:
// a pointer to a timer object
wxTimer *m_timer;
unsigned int m_uiLength; double m_Angle; double m_AngleVelocity;
enum wxIDs
{
ID_WXTIMER1 = 1001,
ID_DUMMY_VALUE_
};
void OnClose(wxCloseEvent& event);
void CreateGUIControls();
DECLARE_EVENT_TABLE()
};
- endif // __wxPendulumDlg_h__
</lang> File wxPendulumDlg.cpp <lang cpp> // --------------------- /// @author Martin Ettl /// @date 2013-02-03 // ---------------------
- include "wxPendulumDlg.hpp"
- include <wx/pen.h>
IMPLEMENT_APP(wxPendulumDlgApp)
bool wxPendulumDlgApp::OnInit() {
wxPendulumDlg* dialog = new wxPendulumDlg(NULL); SetTopWindow(dialog); dialog->Show(true); return true;
}
int wxPendulumDlgApp::OnExit() {
return 0;
}
BEGIN_EVENT_TABLE(wxPendulumDlg, wxDialog)
EVT_CLOSE(wxPendulumDlg::OnClose) EVT_SIZE(wxPendulumDlg::wxPendulumDlgSize) EVT_PAINT(wxPendulumDlg::wxPendulumDlgPaint) EVT_TIMER(ID_WXTIMER1, wxPendulumDlg::OnTimer)
END_EVENT_TABLE()
wxPendulumDlg::wxPendulumDlg(wxWindow *parent, wxWindowID id, const wxString &title, const wxPoint &position, const wxSize& size, long style)
: wxDialog(parent, id, title, position, size, style)
{
CreateGUIControls();
}
wxPendulumDlg::~wxPendulumDlg() { }
void wxPendulumDlg::CreateGUIControls() {
SetIcon(wxNullIcon); SetSize(8, 8, 509, 412); Center();
m_uiLength = 200; m_Angle = M_PI/2.; m_AngleVelocity = 0;
m_timer = new wxTimer(); m_timer->SetOwner(this, ID_WXTIMER1); m_timer->Start(20);
}
void wxPendulumDlg::OnClose(wxCloseEvent& WXUNUSED(event)) {
Destroy();
}
void wxPendulumDlg::wxPendulumDlgPaint(wxPaintEvent& WXUNUSED(event)) {
SetBackgroundStyle(wxBG_STYLE_CUSTOM); wxBufferedPaintDC dc(this);
// Get window dimensions wxSize sz = GetClientSize();
// determine the center of the canvas
const wxPoint center(wxPoint(sz.x / 2, sz.y / 2));
// create background color wxColour powderblue = wxColour(176,224,230);
// draw powderblue background dc.SetPen(powderblue); dc.SetBrush(powderblue); dc.DrawRectangle(0, 0, sz.x, sz.y);
// draw lines
wxPen Pen(*wxBLACK_PEN); Pen.SetWidth(1);
dc.SetPen(Pen); dc.SetBrush(*wxBLACK_BRUSH);
double angleAccel, dt = 0.15;
angleAccel = (-9.81 / m_uiLength) * sin(m_Angle); m_AngleVelocity += angleAccel * dt; m_Angle += m_AngleVelocity * dt;
int anchorX = sz.x / 2, anchorY = sz.y / 4; int ballX = anchorX + (int)(sin(m_Angle) * m_uiLength); int ballY = anchorY + (int)(cos(m_Angle) * m_uiLength); dc.DrawLine(anchorX, anchorY, ballX, ballY);
dc.SetBrush(*wxGREY_BRUSH); dc.DrawEllipse(anchorX - 3, anchorY - 4, 7, 7);
dc.SetBrush(wxColour(255,255,0)); // yellow dc.DrawEllipse(ballX - 7, ballY - 7, 20, 20);
}
void wxPendulumDlg::wxPendulumDlgSize(wxSizeEvent& WXUNUSED(event)) {
Refresh();
}
void wxPendulumDlg::OnTimer(wxTimerEvent& WXUNUSED(event))
{
// force refresh
Refresh();
}
</lang>
This program is tested with wxWidgets version 2.8 and 2.9.
The whole project, including makefile for compiling on Linux
can be download from github.
Clojure
Clojure solution using an atom and a separate rendering thread
<lang clojure> (ns pendulum
(:import (javax.swing JFrame) (java.awt Canvas Graphics Color)))
(def length 200) (def width (* 2 (+ 50 length))) (def height (* 3 (/ length 2))) (def dt 0.1) (def g 9.812) (def k (- (/ g length))) (def anchor-x (/ width 2)) (def anchor-y (/ height 8)) (def angle (atom (/ (Math/PI) 2)))
(defn draw [#^Canvas canvas angle]
(let [buffer (.getBufferStrategy canvas)
g (.getDrawGraphics buffer)
ball-x (+ anchor-x (* (Math/sin angle) length))
ball-y (+ anchor-y (* (Math/cos angle) length))]
(try
(doto g
(.setColor Color/BLACK)
(.fillRect 0 0 width height)
(.setColor Color/RED)
(.drawLine anchor-x anchor-y ball-x ball-y)
(.setColor Color/YELLOW)
(.fillOval (- anchor-x 3) (- anchor-y 4) 7 7)
(.fillOval (- ball-x 7) (- ball-y 7) 14 14))
(finally (.dispose g)))
(if-not (.contentsLost buffer)
(.show buffer)) ))
(defn start-renderer [canvas]
(->> (fn [] (draw canvas @angle) (recur)) (new Thread) (.start)))
(defn -main [& args]
(let [frame (JFrame. "Pendulum")
canvas (Canvas.)]
(doto frame
(.setSize width height)
(.setDefaultCloseOperation JFrame/EXIT_ON_CLOSE)
(.setResizable false)
(.add canvas)
(.setVisible true))
(doto canvas
(.createBufferStrategy 2)
(.setVisible true)
(.requestFocus))
(start-renderer canvas)
(loop [v 0]
(swap! angle #(+ % (* v dt)))
(Thread/sleep 15)
(recur (+ v (* k (Math/sin @angle) dt)))) ))
(-main) </lang>
Common Lisp
An approach using closures. Physics code adapted from Ada.
Pressing the spacebar adds a pendulum.
<lang lisp>(defvar *frame-rate* 30) (defvar *damping* 0.99 "Deceleration factor.")
(defun make-pendulum (length theta0 x)
"Returns an anonymous function with enclosed state representing a pendulum."
(let* ((theta (* (/ theta0 180) pi))
(acceleration 0))
(if (< length 40) (setf length 40)) ;;avoid a divide-by-zero
(lambda ()
;;Draws the pendulum, updating its location and speed.
(sdl:draw-line (sdl:point :x x :y 1)
(sdl:point :x (+ (* (sin theta) length) x)
:y (* (cos theta) length)))
(sdl:draw-filled-circle (sdl:point :x (+ (* (sin theta) length) x)
:y (* (cos theta) length))
20
:color sdl:*yellow*
:stroke-color sdl:*white*)
;;The magic constant approximates the speed we want for a given frame-rate.
(incf acceleration (* (sin theta) (* *frame-rate* -0.001)))
(incf theta acceleration)
(setf acceleration (* acceleration *damping*)))))
(defun main (&optional (w 640) (h 480))
(sdl:with-init ()
(sdl:window w h :title-caption "Pendulums"
:fps (make-instance 'sdl:fps-fixed))
(setf (sdl:frame-rate) *frame-rate*)
(let ((pendulums nil))
(sdl:with-events ()
(:quit-event () t)
(:idle ()
(sdl:clear-display sdl:*black*)
(mapcar #'funcall pendulums) ;;Draw all the pendulums
(sdl:update-display))
(:key-down-event (:key key)
(cond ((sdl:key= key :sdl-key-escape)
(sdl:push-quit-event))
((sdl:key= key :sdl-key-space)
(push (make-pendulum (random (- h 100))
(random 90)
(round w 2))
pendulums))))))))</lang>
Delphi
<lang Delphi> unit main;
interface
uses
Vcl.Forms, Vcl.Graphics, Vcl.ExtCtrls;
type
TForm1 = class(TForm) procedure FormCreate(Sender: TObject); procedure FormDestroy(Sender: TObject); private Timer: TTimer; angle, angleAccel, angleVelocity, dt: double; len: Integer; procedure Tick(Sender: TObject); end;
var
Form1: TForm1;
implementation
{$R *.dfm}
procedure TForm1.FormCreate(Sender: TObject); begin
Width := 200; Height := 200; DoubleBuffered := True; Timer := TTimer.Create(nil); Timer.Interval := 30; Timer.OnTimer := Tick; Caption := 'Pendulum';
// initialize angle := PI / 2; angleAccel := 0; angleVelocity := 0; dt := 0.1; len := 50;
end;
procedure TForm1.FormDestroy(Sender: TObject); begin
Timer.Free;
end;
procedure TForm1.Tick(Sender: TObject); const
HalfPivot = 4; HalfBall = 7;
var
anchorX, anchorY, ballX, ballY: Integer;
begin
anchorX := Width div 2 - 12; anchorY := Height div 4; ballX := anchorX + Trunc(Sin(angle) * len); ballY := anchorY + Trunc(Cos(angle) * len);
angleAccel := -9.81 / len * Sin(angle); angleVelocity := angleVelocity + angleAccel * dt; angle := angle + angleVelocity * dt;
with canvas do begin Pen.Color := clBlack;
with Brush do
begin
Style := bsSolid;
Color := clWhite;
end;
FillRect(ClientRect); MoveTo(anchorX, anchorY); LineTo(ballX, ballY);
Brush.Color := clGray;
Ellipse(anchorX - HalfPivot, anchorY - HalfPivot, anchorX + HalfPivot,
anchorY + HalfPivot);
Brush.Color := clYellow; Ellipse(ballX - HalfBall, ballY - HalfBall, ballX + HalfBall, ballY + HalfBall); end;
end;
end.</lang>
E
(Uses Java Swing for GUI. The animation logic is independent, however.)
The angle of a pendulum with length and acceleration due to gravity with all its mass at the end and no friction/air resistance has an acceleration at any given moment of
This simulation uses this formula directly, updating the velocity from the acceleration and the position from the velocity; inaccuracy results from the finite timestep.
The event flow works like this:
The clock object created by the simulation steps the simulation on the specified in the interval.
The simulation writes its output to angle, which is a Lamport slot which can notify of updates.
The whenever set up by makeDisplayComponent listens for updates and triggers redrawing as long as interest has been expressed, which is done whenever the component actually redraws, which happens only if the component's window is still on screen.
When the window is closed, additionally, the simulation itself is stopped and the application allowed to exit.
(This logic is more general than necessary; it is designed to be suitable for a larger application as well.)
<lang e>#!/usr/bin/env rune pragma.syntax("0.9")
def pi := (-1.0).acos() def makeEPainter := <unsafe:com.zooko.tray.makeEPainter> def makeLamportSlot := <import:org.erights.e.elib.slot.makeLamportSlot> def whenever := <import:org.erights.e.elib.slot.whenever> def colors := <import:java.awt.makeColor>
- --------------------------------------------------------------
- --- Definitions
def makePendulumSim(length_m :float64,
gravity_mps2 :float64,
initialAngle_rad :float64,
timestep_ms :int) {
var velocity := 0
def &angle := makeLamportSlot(initialAngle_rad)
def k := -gravity_mps2/length_m
def timestep_s := timestep_ms / 1000
def clock := timer.every(timestep_ms, fn _ {
def acceleration := k * angle.sin()
velocity += acceleration * timestep_s
angle += velocity * timestep_s
})
return [clock, &angle]
}
def makeDisplayComponent(&angle) {
def c
def updater := whenever([&angle], fn { c.repaint() })
bind c := makeEPainter(def paintCallback {
to paintComponent(g) {
try {
def originX := c.getWidth() // 2
def originY := c.getHeight() // 2
def pendRadius := (originX.min(originY) * 0.95).round()
def ballRadius := (originX.min(originY) * 0.04).round()
def ballX := (originX + angle.sin() * pendRadius).round()
def ballY := (originY + angle.cos() * pendRadius).round()
g.setColor(colors.getWhite())
g.fillRect(0, 0, c.getWidth(), c.getHeight())
g.setColor(colors.getBlack())
g.fillOval(originX - 2, originY - 2, 4, 4)
g.drawLine(originX, originY, ballX, ballY)
g.fillOval(ballX - ballRadius, ballY - ballRadius, ballRadius * 2, ballRadius * 2)
updater[] # provoke interest provided that we did get drawn (window not closed)
} catch p {
stderr.println(`In paint callback: $p${p.eStack()}`)
}
}
})
c.setPreferredSize(<awt:makeDimension>(300, 300))
return c
}
- --------------------------------------------------------------
- --- Application setup
def [clock, &angle] := makePendulumSim(1, 9.80665, pi*99/100, 10)
- Initialize AWT, move to AWT event thread
when (currentVat.morphInto("awt")) -> {
# Create the window
def frame := <unsafe:javax.swing.makeJFrame>("Pendulum")
frame.setContentPane(def display := makeDisplayComponent(&angle))
frame.addWindowListener(def mainWindowListener {
to windowClosing(_) {
clock.stop()
interp.continueAtTop()
}
match _ {}
})
frame.setLocation(50, 50)
frame.pack()
# Start and become visible frame.show() clock.start()
}
interp.blockAtTop()</lang>
EasyLang
<lang>on animate
clear_screen move_pen 50 50 draw_circle 1 x = 50 + 40 * sin ang y = 50 - 40 * cos ang draw_line x y draw_circle 5 vel += sin ang / 5 ang += vel
. ang = 10</lang>
Elm
<lang elm>import Color exposing (..) import Collage exposing (..) import Element exposing (..) import Html exposing (..) import Time exposing (..) import Html.App exposing (program)
dt = 0.01 scale = 100
type alias Model =
{ angle : Float
, angVel : Float
, length : Float
, gravity : Float
}
type Msg
= Tick Time
init : (Model,Cmd Msg) init =
( { angle = 3 * pi / 4
, angVel = 0.0
, length = 2
, gravity = -9.81
}
, Cmd.none)
update : Msg -> Model -> (Model, Cmd Msg) update _ model =
let
angAcc = -1.0 * (model.gravity / model.length) * sin (model.angle)
angVel' = model.angVel + angAcc * dt
angle' = model.angle + angVel' * dt
in
( { model
| angle = angle'
, angVel = angVel'
}
, Cmd.none )
view : Model -> Html Msg view model =
let
endPoint = ( 0, scale * model.length )
pendulum =
group
[ segment ( 0, 0 ) endPoint
|> traced { defaultLine | width = 2, color = red }
, circle 8
|> filled blue
, ngon 3 10
|> filled green
|> rotate (pi/2)
|> move endPoint
]
in
toHtml <|
collage 700 500
[ pendulum |> rotate model.angle ]
subscriptions : Model -> Sub Msg subscriptions _ =
Time.every (dt * second) Tick
main =
program
{ init = init
, view = view
, update = update
, subscriptions = subscriptions
}</lang>
Link to live demo: http://dc25.github.io/animatedPendulumElm
ERRE
<lang ERRE> PROGRAM PENDULUM
! ! for rosettacode.org !
!$KEY
!$INCLUDE="PC.LIB"
PROCEDURE PENDULUM(A,L)
PIVOTX=320
PIVOTY=0
BOBX=PIVOTX+L*500*SIN(a)
BOBY=PIVOTY+L*500*COS(a)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,6,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,11)
PAUSE(0.01)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,0,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,0)
END PROCEDURE
BEGIN
SCREEN(9)
THETA=40*p/180 ! initial displacement
G=9.81 ! acceleration due to gravity
L=0.5 ! length of pendulum in metres
LINE(0,0,639,0,5,FALSE)
LOOP
PENDULUM(THETA,L)
ACCEL=-G*SIN(THETA)/L/100
SPEED=SPEED+ACCEL/100
THETA=THETA+SPEED
END LOOP
END PROGRAM </lang> PC version: Ctrl+Break to stop.
Euler Math Toolbox
Euler Math Toolbox can determine the exact period of a physical pendulum. The result is then used to animate the pendulum. The following code is ready to be pasted back into Euler notebooks.
>g=gearth$; l=1m;
>function f(x,y) := [y[2],-g*sin(y[1])/l]
>function h(a) := ode("f",linspace(0,a,100),[0,2])[1,-1]
>period=solve("h",2)
2.06071780729
>t=linspace(0,period,30); s=ode("f",t,[0,2])[1];
>function anim (t,s) ...
$ setplot(-1,1,-1,1);
$ markerstyle("o#");
$ repeat
$ for i=1 to cols(t)-1;
$ clg;
$ hold on;
$ plot([0,sin(s[i])],[1,1-cos(s[i])]);
$ mark([0,sin(s[i])],[1,1-cos(s[i])]);
$ hold off;
$ wait(t[i+1]-t[i]);
$ end;
$ until testkey();
$ end
$endfunction
>anim(t,s);
>
Euphoria
DOS32 version
<lang euphoria>include graphics.e include misc.e
constant dt = 1E-3 constant g = 50
sequence vc sequence suspension atom len
procedure draw_pendulum(atom color, atom len, atom alfa)
sequence point
point = (len*{sin(alfa),cos(alfa)} + suspension)
draw_line(color, {suspension, point})
ellipse(color,0,point-{10,10},point+{10,10})
end procedure
function wait()
atom t0
t0 = time()
while time() = t0 do
if get_key() != -1 then
return 1
end if
end while
return 0
end function
procedure animation()
atom alfa, omega, epsilon
if graphics_mode(18) then
end if
vc = video_config()
suspension = {vc[VC_XPIXELS]/2,vc[VC_YPIXELS]/2}
len = vc[VC_YPIXELS]/2-20
alfa = PI/2
omega = 0
while 1 do
draw_pendulum(BRIGHT_WHITE,len,alfa)
if wait() then
exit
end if
draw_pendulum(BLACK,len,alfa)
epsilon = -len*sin(alfa)*g
omega += dt*epsilon
alfa += dt*omega
end while
if graphics_mode(-1) then end if
end procedure
animation()</lang>
F#
A nice application of F#'s support for units of measure. <lang fsharp>open System open System.Drawing open System.Windows.Forms
// define units of measurement [<Measure>] type m; // metres [<Measure>] type s; // seconds
// a pendulum is represented as a record of physical quantities type Pendulum =
{ length : float<m>
gravity : float<m/s^2>
velocity : float<m/s>
angle : float
}
// calculate the next state of a pendulum let next pendulum deltaT : Pendulum =
let k = -pendulum.gravity / pendulum.length
let acceleration = k * Math.Sin pendulum.angle * 1.0<m>
let newVelocity = pendulum.velocity + acceleration * deltaT
let newAngle = pendulum.angle + newVelocity * deltaT / 1.0<m>
{ pendulum with velocity = newVelocity; angle = newAngle }
// paint a pendulum (using hard-coded screen coordinates) let paint pendulum (gr: System.Drawing.Graphics) =
let homeX = 160 let homeY = 50 let length = 140.0 // draw plate gr.DrawLine( new Pen(Brushes.Gray, width=2.0f), 0, homeY, 320, homeY ) // draw pivot gr.FillEllipse( Brushes.Gray, homeX-5, homeY-5, 10, 10 ) gr.DrawEllipse( new Pen(Brushes.Black), homeX-5, homeY-5, 10, 10 ) // draw the pendulum itself let x = homeX + int( length * Math.Sin pendulum.angle ) let y = homeY + int( length * Math.Cos pendulum.angle ) // draw rod gr.DrawLine( new Pen(Brushes.Black, width=3.0f), homeX, homeY, x, y ) // draw bob gr.FillEllipse( Brushes.Yellow, x-15, y-15, 30, 30 ) gr.DrawEllipse( new Pen(Brushes.Black), x-15, y-15, 30, 30 )
// defines an operator "-?" that calculates the time from t2 to t1
// where t2 is optional
let (-?) (t1: DateTime) (t2: DateTime option) : float =
match t2 with | None -> 0.0// only one timepoint given -> difference is 0 | Some t -> (t1 - t).TotalSeconds * 1.0
// our main window is double-buffered form that reacts to paint events type PendulumForm() as self =
inherit Form(Width=325, Height=240, Text="Pendulum")
let mutable pendulum = { length = 1.0<m>;
gravity = 9.81<m/s^2>
velocity = 0.0<m/s>
angle = Math.PI / 2.0
}
let mutable lastPaintedAt = None
let updateFreq = 0.01
do self.DoubleBuffered <- true
self.Paint.Add( fun args ->
let now = DateTime.Now
let deltaT = now -? lastPaintedAt |> min 0.01
lastPaintedAt <- Some now
pendulum <- next pendulum deltaT
let gr = args.Graphics
gr.Clear( Color.LightGray )
paint pendulum gr
// initiate a new paint event after a while (non-blocking)
async { do! Async.Sleep( int( 1000.0 * updateFreq / 1.0 ) )
self.Invalidate()
}
|> Async.Start
)
[<STAThread>] Application.Run( new PendulumForm( Visible=true ) )</lang>
Factor
Approximation of the pendulum for small swings : theta = theta0 * cos(omega0 * t) <lang factor>USING: accessors alarms arrays calendar colors.constants kernel locals math math.constants math.functions math.rectangles math.vectors opengl sequences system ui ui.gadgets ui.render ; IN: pendulum
CONSTANT: g 9.81 CONSTANT: l 20 CONSTANT: theta0 0.5
- current-time ( -- time ) nano-count -9 10^ * ;
- T0 ( -- T0 ) 2 pi l g / sqrt * * ;
- omega0 ( -- omega0 ) 2 pi * T0 / ;
- theta ( -- theta ) current-time omega0 * cos theta0 * ;
- relative-xy ( theta l -- xy )
swap [ sin * ] [ cos * ] 2bi 2array ;
- theta-to-xy ( origin theta l -- xy ) relative-xy v+ ;
TUPLE: pendulum-gadget < gadget alarm ;
- O ( gadget -- origin ) rect-bounds [ drop ] [ first 2 / ] bi* 0 2array ;
- window-l ( gadget -- l ) rect-bounds [ drop ] [ second ] bi* ;
- gadget-xy ( gadget -- xy ) [ O ] [ drop theta ] [ window-l ] tri theta-to-xy ;
M: pendulum-gadget draw-gadget*
COLOR: black gl-color [ O ] [ gadget-xy ] bi gl-line ;
M:: pendulum-gadget graft* ( gadget -- )
[ gadget relayout-1 ] 20 milliseconds every gadget (>>alarm) ;
M: pendulum-gadget ungraft* alarm>> cancel-alarm ;
- <pendulum-gadget> ( -- gadget )
pendulum-gadget new
{ 500 500 } >>pref-dim ;
- pendulum-main ( -- )
[ <pendulum-gadget> "pendulum" open-window ] with-ui ;
MAIN: pendulum-main </lang>
FBSL
<lang qbasic>#INCLUDE <Include\Windows.inc>
FBSLSETTEXT(ME, "Pendulum") FBSL.SETTIMER(ME, 1000, 10) RESIZE(ME, 0, 0, 300, 200) CENTER(ME) SHOW(ME)
BEGIN EVENTS SELECT CASE CBMSG CASE WM_TIMER ' Request redraw InvalidateRect(ME, NULL, FALSE) RETURN 0 CASE WM_PAINT Swing() CASE WM_CLOSE FBSL.KILLTIMER(ME, 1000) END SELECT END EVENTS
SUB Swing() TYPE RECT: %rcLeft, %rcTop, %rcRight, %rcBottom: END TYPE STATIC rc AS RECT, !!acceleration, !!velocity, !!angle = M_PI_2, %pendulum = 100
GetClientRect(ME, @rc)
' Recalculate DIM headX = rc.rcRight / 2, headY = rc.rcBottom / 4 DIM tailX = headX + SIN(angle) * pendulum DIM tailY = headY + COS(angle) * pendulum
acceleration = -9.81 / pendulum * SIN(angle) INCR(velocity, acceleration * 0.1)(angle, velocity * 0.1)
' Create backbuffer CreateCompatibleDC(GetDC(ME)) SelectObject(CreateCompatibleDC, CreateCompatibleBitmap(GetDC, rc.rcRight, rc.rcBottom))
' Draw to backbuffer FILLSTYLE(FILL_SOLID): FILLCOLOR(RGB(200, 200, 0)) LINE(CreateCompatibleDC, 0, 0, rc.rcRight, rc.rcBottom, GetSysColor(COLOR_BTNHILIGHT), TRUE, TRUE) LINE(CreateCompatibleDC, 0, headY, rc.rcRight, headY, GetSysColor(COLOR_3DSHADOW)) DRAWWIDTH(3) LINE(CreateCompatibleDC, headX, headY, tailX, tailY, RGB(200, 0, 0)) DRAWWIDTH(1) CIRCLE(CreateCompatibleDC, headX, headY, 2, GetSysColor, 0, 360, 1, TRUE) CIRCLE(CreateCompatibleDC, tailX, tailY, 10, GetSysColor, 0, 360, 1, FALSE)
' Blit to window BitBlt(GetDC, 0, 0, rc.rcRight, rc.rcBottom, CreateCompatibleDC, 0, 0, SRCCOPY) ReleaseDC(ME, GetDC)
' Delete backbuffer DeleteObject(SelectObject(CreateCompatibleDC, SelectObject)) DeleteDC(CreateCompatibleDC) END SUB</lang> Screenshot:
Fortran
Uses system commands (gfortran) to clear the screen. An initial starting angle is allowed between 90 (to the right) and -90 degrees (to the left). It checks for incorrect inputs. <lang fortran> !Implemented by Anant Dixit (October, 2014) program animated_pendulum implicit none double precision, parameter :: pi = 4.0D0*atan(1.0D0), l = 1.0D-1, dt = 1.0D-2, g = 9.8D0 integer :: io double precision :: s_ang, c_ang, p_ang, n_ang
write(*,*) 'Enter starting angle (in degrees):' do
read(*,*,iostat=io) s_ang if(io.ne.0 .or. s_ang.lt.-90.0D0 .or. s_ang.gt.90.0D0) then write(*,*) 'Please enter an angle between 90 and -90 degrees:' else exit end if
end do call execute_command_line('cls')
c_ang = s_ang*pi/180.0D0 p_ang = c_ang
call display(c_ang) do
call next_time_step(c_ang,p_ang,g,l,dt,n_ang)
if(abs(c_ang-p_ang).ge.0.05D0) then
call execute_command_line('cls')
call display(c_ang)
end if
end do end program
subroutine next_time_step(c_ang,p_ang,g,l,dt,n_ang) double precision :: c_ang, p_ang, g, l, dt, n_ang n_ang = (-g*sin(c_ang)/l)*2.0D0*dt**2 + 2.0D0*c_ang - p_ang p_ang = c_ang c_ang = n_ang end subroutine
subroutine display(c_ang) double precision :: c_ang character (len=*), parameter :: cfmt = '(A1)' double precision :: rx, ry integer :: x, y, i, j rx = 45.0D0*sin(c_ang) ry = 22.5D0*cos(c_ang) x = int(rx)+51 y = int(ry)+2 do i = 1,32
do j = 1,100
if(i.eq.y .and. j.eq.x) then
write(*,cfmt,advance='no') 'O'
else if(i.eq.y .and. (j.eq.(x-1).or.j.eq.(x+1))) then
write(*,cfmt,advance='no') 'G'
else if(j.eq.x .and. (i.eq.(y-1).or.i.eq.(y+1))) then
write(*,cfmt,advance='no') 'G'
else if(i.eq.y .and. (j.eq.(x-2).or.j.eq.(x+2))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.x .and. (i.eq.(y-2).or.i.eq.(y+2))) then
write(*,cfmt,advance='no') 'G'
else if((i.eq.(y+1).and.j.eq.(x+1)) .or. (i.eq.(y-1).and.j.eq.(x-1))) then
write(*,cfmt,advance='no') '#'
else if((i.eq.(y+1).and.j.eq.(x-1)) .or. (i.eq.(y-1).and.j.eq.(x+1))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.50) then
write(*,cfmt,advance='no') '|'
else if(i.eq.2) then
write(*,cfmt,advance='no') '-'
else
write(*,cfmt,advance='no') ' '
end if
end do
write(*,*)
end do end subroutine </lang>
A small preview (truncated to a few steps of the pendulum changing direction). Initial angle provided = 80 degrees.
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Groovy
Straight translation of Java solution groovified by removing explicit definitions and converting casts to Groovy as style where needed. <lang groovy> import java.awt.*; import javax.swing.*;
class Pendulum extends JPanel implements Runnable {
private angle = Math.PI / 2; private length;
Pendulum(length) {
this.length = length;
setDoubleBuffered(true);
}
@Override
void paint(Graphics g) {
g.setColor(Color.WHITE);
g.fillRect(0, 0, getWidth(), getHeight());
g.setColor(Color.BLACK);
int anchorX = getWidth() / 2, anchorY = getHeight() / 4;
def ballX = anchorX + (Math.sin(angle) * length) as int;
def ballY = anchorY + (Math.cos(angle) * length) as int;
g.drawLine(anchorX, anchorY, ballX, ballY);
g.fillOval(anchorX - 3, anchorY - 4, 7, 7);
g.fillOval(ballX - 7, ballY - 7, 14, 14);
}
void run() {
def angleAccel, angleVelocity = 0, dt = 0.1;
while (true) {
angleAccel = -9.81 / length * Math.sin(angle);
angleVelocity += angleAccel * dt;
angle += angleVelocity * dt;
repaint();
try { Thread.sleep(15); } catch (InterruptedException ex) {}
}
}
@Override
Dimension getPreferredSize() {
return new Dimension(2 * length + 50, (length / 2 * 3) as int);
}
static void main(String[] args) {
def f = new JFrame("Pendulum");
def p = new Pendulum(200);
f.add(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setVisible(true);
new Thread(p).start();
}
} </lang>
Go
Using
from Github
<lang go>package main
import ( "github.com/google/gxui" "github.com/google/gxui/drivers/gl" "github.com/google/gxui/math" "github.com/google/gxui/themes/dark" omath "math" "time" )
//Two pendulums animated //Top: Mathematical pendulum with small-angle approxmiation (not appropiate with PHI_ZERO=pi/2) //Bottom: Simulated with differential equation phi = g/l * sin(phi)
const ( ANIMATION_WIDTH int = 480 ANIMATION_HEIGHT int = 320 BALL_RADIUS float32 = 25.0 METER_PER_PIXEL float64 = 1.0 / 20.0 PHI_ZERO float64 = omath.Pi * 0.5 )
var ( l float64 = float64(ANIMATION_HEIGHT) * 0.5 freq float64 = omath.Sqrt(9.81 / (l * METER_PER_PIXEL)) )
type Pendulum interface { GetPhi() float64 }
type mathematicalPendulum struct { start time.Time }
func (p *mathematicalPendulum) GetPhi() float64 { if (p.start == time.Time{}) { p.start = time.Now() } t := float64(time.Since(p.start).Nanoseconds()) / omath.Pow10(9) return PHI_ZERO * omath.Cos(t*freq) }
type numericalPendulum struct { currentPhi float64 angAcc float64 angVel float64 lastTime time.Time }
func (p *numericalPendulum) GetPhi() float64 { dt := 0.0 if (p.lastTime != time.Time{}) { dt = float64(time.Since(p.lastTime).Nanoseconds()) / omath.Pow10(9) } p.lastTime = time.Now()
p.angAcc = -9.81 / (float64(l) * METER_PER_PIXEL) * omath.Sin(p.currentPhi) p.angVel += p.angAcc * dt p.currentPhi += p.angVel * dt
return p.currentPhi }
func draw(p Pendulum, canvas gxui.Canvas, x, y int) { attachment := math.Point{X: ANIMATION_WIDTH/2 + x, Y: y}
phi := p.GetPhi() ball := math.Point{X: x + ANIMATION_WIDTH/2 + math.Round(float32(l*omath.Sin(phi))), Y: y + math.Round(float32(l*omath.Cos(phi)))}
line := gxui.Polygon{gxui.PolygonVertex{attachment, 0}, gxui.PolygonVertex{ball, 0}}
canvas.DrawLines(line, gxui.DefaultPen)
m := math.Point{int(BALL_RADIUS), int(BALL_RADIUS)} rect := math.Rect{ball.Sub(m), ball.Add(m)} canvas.DrawRoundedRect(rect, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, gxui.TransparentPen, gxui.CreateBrush(gxui.Yellow)) }
func appMain(driver gxui.Driver) { theme := dark.CreateTheme(driver)
window := theme.CreateWindow(ANIMATION_WIDTH, 2*ANIMATION_HEIGHT, "Pendulum") window.SetBackgroundBrush(gxui.CreateBrush(gxui.Gray50))
image := theme.CreateImage()
ticker := time.NewTicker(time.Millisecond * 15) pendulum := &mathematicalPendulum{} pendulum2 := &numericalPendulum{PHI_ZERO, 0.0, 0.0, time.Time{}}
go func() { for _ = range ticker.C { canvas := driver.CreateCanvas(math.Size{ANIMATION_WIDTH, 2 * ANIMATION_HEIGHT}) canvas.Clear(gxui.White)
draw(pendulum, canvas, 0, 0) draw(pendulum2, canvas, 0, ANIMATION_HEIGHT)
canvas.Complete() driver.Call(func() { image.SetCanvas(canvas) }) } }()
window.AddChild(image)
window.OnClose(ticker.Stop) window.OnClose(driver.Terminate) }
func main() { gl.StartDriver(appMain) }</lang>
Haskell
<lang haskell>import Graphics.HGL.Draw.Monad (Graphic, ) import Graphics.HGL.Draw.Picture import Graphics.HGL.Utils import Graphics.HGL.Window import Graphics.HGL.Run
import Control.Exception (bracket, ) import Control.Arrow
toInt = fromIntegral.round
pendulum = runGraphics $
bracket
(openWindowEx "Pendulum animation task" Nothing (600,400) DoubleBuffered (Just 30))
closeWindow
(\w -> mapM_ ((\ g -> setGraphic w g >> getWindowTick w).
(\ (x, y) -> overGraphic (line (300, 0) (x, y))
(ellipse (x - 12, y + 12) (x + 12, y - 12)) )) pts)
where
dt = 1/30
t = - pi/4
l = 1
g = 9.812
nextAVT (a,v,t) = (a', v', t + v' * dt) where
a' = - (g / l) * sin t
v' = v + a' * dt
pts = map (\(_,t,_) -> (toInt.(300+).(300*).cos &&& toInt. (300*).sin) (pi/2+0.6*t) )
$ iterate nextAVT (- (g / l) * sin t, t, 0)</lang>
Usage with ghci:
*Main> pendulum
Alternative solution
<lang haskell>import Graphics.Gloss
-- Initial conditions g_ = (-9.8) :: Float --Gravity acceleration v_0 = 0 :: Float --Initial tangential speed a_0 = 0 / 180 * pi :: Float --Initial angle dt = 0.01 :: Float --Time step t_f = 15 :: Float --Final time for data logging l_ = 200 :: Float --Rod length
-- Define a type to represent the pendulum: type Pendulum = (Float, Float, Float) -- (rod length, tangential speed, angle)
-- Pendulum's initial state initialstate :: Pendulum initialstate = (l_, v_0, a_0)
-- Step funtion: update pendulum to new position movePendulum :: Float -> Pendulum -> Pendulum movePendulum dt (l,v,a) = ( l , v_2 , a + v_2 / l * dt*10 )
where v_2 = v + g_ * (cos a) * dt
-- Convert from Pendulum to [Picture] for display renderPendulum :: Pendulum -> [Picture] renderPendulum (l,v,a) = map (uncurry Translate newOrigin)
[ Line [ ( 0 , 0 ) , ( l * (cos a), l * (sin a) ) ]
, polygon [ ( 0 , 0 ) , ( -5 , 8.66 ) , ( 5 , 8.66 ) ]
, Translate ( l * (cos a)) (l * (sin a)) (circleSolid (0.04*l_))
, Translate (-1.1*l) (-1.3*l) (Scale 0.1 0.1 (Text currSpeed))
, Translate (-1.1*l) (-1.3*l + 20) (Scale 0.1 0.1 (Text currAngle))
]
where currSpeed = "Speed (pixels/s) = " ++ (show v)
currAngle = "Angle (deg) = " ++ (show ( 90 + a / pi * 180 ) )
-- New origin to beter display the animation newOrigin = (0, l_ / 2)
-- Calcule a proper window size (for angles between 0 and -pi) windowSize :: (Int, Int) windowSize = ( 300 + 2 * round (snd newOrigin)
, 200 + 2 * round (snd newOrigin) )
-- Run simulation main :: IO () main = do --plotOnGNU
simulate window background fps initialstate render update
where window = InWindow "Animate a pendulum" windowSize (40, 40)
background = white
fps = round (1/dt)
render xs = pictures $ renderPendulum xs
update _ = movePendulum</lang>
HicEst
DIFFEQ and the callback procedure pendulum numerically integrate the pendulum equation. The display window can be resized during the run, but for window width not equal to 2*height the pendulum rod becomes a rubber band instead: <lang HicEst>REAL :: msec=10, Lrod=1, dBob=0.03, g=9.81, Theta(2), dTheta(2) BobMargins = ALIAS(ls, rs, ts, bs) ! box margins to draw the bob
Theta = (1, 0) ! initial angle and velocity
start_t = TIME()
DO i = 1, 1E100 ! "forever"
end_t = TIME() ! to integrate in real-time sections: DIFFEQ(Callback="pendulum", T=end_t, Y=Theta, DY=dTheta, T0=start_t) xBob = (SIN(Theta(1)) + 1) / 2 yBob = COS(Theta(1)) - dBob
! create or clear window and draw pendulum bob at (xBob, yBob): WINDOW(WIN=wh, LeftSpace=0, RightSpace=0, TopSpace=0, BottomSpace=0, Up=999) BobMargins = (xBob-dBob, 1-xBob-dBob, yBob-dBob, 1-yBob-dBob) WINDOW(WIN=wh, LeftSpace=ls, RightSpace=rs, TopSpace=ts, BottomSpace=bs) WRITE(WIN=wh, DeCoRation='EL=4, BC=4') ! flooded red ellipse as bob
! draw the rod hanging from the center of the window: WINDOW(WIN=wh, LeftSpace=0.5, TopSpace=0, RightSpace=rs+dBob) WRITE(WIN=wh, DeCoRation='LI=0 0; 1 1, FC=4.02') ! red pendulum rod
SYSTEM(WAIT=msec) start_t = end_t
ENDDO
END
SUBROUTINE pendulum ! Theta" = - (g/Lrod) * SIN(Theta)
dTheta(1) = Theta(2) ! Theta' = Theta(2) substitution dTheta(2) = -g/Lrod*SIN(Theta(1)) ! Theta" = Theta(2)' = -g/Lrod*SIN(Theta(1))
END</lang>
Icon and Unicon
The following code uses features exclusive to Unicon, specifically the object-oriented gui library.
<lang Unicon> import gui $include "guih.icn"
- some constants to define the display and pendulum
$define HEIGHT 400 $define WIDTH 500 $define STRING_LENGTH 200 $define HOME_X 250 $define HOME_Y 21 $define SIZE 30 $define START_ANGLE 80
class WindowApp : Dialog ()
# draw the pendulum on given context_window, at position (x,y) method draw_pendulum (x, y) # reference to current screen area to draw on cw := Clone(self.cwin)
# clear screen WAttrib (cw, "bg=grey") EraseRectangle (cw, 0, 0, WIDTH, HEIGHT)
# draw the display WAttrib (cw, "fg=dark gray") DrawLine (cw, 10, 20, WIDTH-20, 20) WAttrib (cw, "fg=black") DrawLine (cw, HOME_X, HOME_Y, x, y) FillCircle (cw, x, y, SIZE+2) WAttrib (cw, "fg=yellow") FillCircle (cw, x, y, SIZE)
# free reference to screen area Uncouple (cw) end
# find the average of given two arguments method avg (a, b) return (a + b) / 2 end
# this method gets called by the ticker # it computes the next position of the pendulum and # requests a redraw method tick () static x, y static theta := START_ANGLE static d_theta := 0 # update x,y of pendulum scaling := 3000.0 / (STRING_LENGTH * STRING_LENGTH) # -- first estimate first_dd_theta := -(sin (dtor (theta)) * scaling) mid_d_theta := d_theta + first_dd_theta mid_theta := theta + avg (d_theta, mid_d_theta) # -- second estimate mid_dd_theta := - (sin (dtor (mid_theta)) * scaling) mid_d_theta_2 := d_theta + avg (first_dd_theta, mid_dd_theta) mid_theta_2 := theta + avg (d_theta, mid_d_theta_2) # -- again first mid_dd_theta_2 := -(sin (dtor (mid_theta_2)) * scaling) last_d_theta := mid_d_theta_2 + mid_dd_theta_2 last_theta := mid_theta_2 + avg (mid_d_theta_2, last_d_theta) # -- again second last_dd_theta := - (sin (dtor (last_theta)) * scaling) last_d_theta_2 := mid_d_theta_2 + avg (mid_dd_theta_2, last_dd_theta) last_theta_2 := mid_theta_2 + avg (mid_d_theta_2, last_d_theta_2) # -- update stored angles d_theta := last_d_theta_2 theta := last_theta_2 # -- update x, y pendulum_angle := dtor (theta) x := HOME_X + STRING_LENGTH * sin (pendulum_angle) y := HOME_Y + STRING_LENGTH * cos (pendulum_angle)
# draw pendulum draw_pendulum (x, y) end
# set up the window
method component_setup ()
# some cosmetic settings for the window
attrib("size="||WIDTH||","||HEIGHT, "bg=light gray", "label=Pendulum")
# make sure we respond to window close event
connect (self, "dispose", CLOSE_BUTTON_EVENT)
# start the ticker, to update the display periodically
self.set_ticker (20)
end
end
procedure main ()
w := WindowApp () w.show_modal ()
end </lang>
J
Works for J6 <lang j>require 'gl2 trig' coinsert 'jgl2'
DT =: %30 NB. seconds ANGLE=: 0.45p1 NB. radians L =: 1 NB. metres G =: 9.80665 NB. ms_2 VEL =: 0 NB. ms_1
PEND=: noun define pc pend;pn "Pendulum"; xywh 0 0 320 200;cc isi isigraph rightmove bottommove; pas 0 0;pcenter; rem form end; )
pend_run =: verb def ' wd PEND,;pshow;timer ,":DT * 1000 ' pend_close =: verb def ' wd timer 0; pclose ' pend_isi_paint=: verb def ' drawPendulum ANGLE '
sys_timer_z_=: verb define
recalcAngle wd 'psel pend; setinvalid isi'
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE VEL =: VEL + accel * DT ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh
ps=. (-: width) , 40
pe=. ps + 280 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glbrush glrgb 91 91 91
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glellipse (,~ pe - -:) 20 20
glrect 0 0 ,width, 40
)
pend_run NB. run animation</lang> Updated for changes in J8 <lang j>require 'gl2 trig' coinsert 'jgl2'
DT =: %30 NB. seconds ANGLE=: 0.45p1 NB. radians L =: 1 NB. metres G =: 9.80665 NB. ms_2 VEL =: 0 NB. ms_1
PEND=: noun define pc pend;pn "Pendulum"; minwh 320 200; cc isi isigraph flush; )
pend_run=: verb define
wd PEND,'pshow' wd 'timer ',":DT * 1000
)
pend_close=: verb define
wd 'timer 0; pclose'
)
sys_timer_z_=: verb define
recalcAngle_base_ wd 'psel pend; set isi invalid'
)
pend_isi_paint=: verb define
drawPendulum ANGLE
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE VEL =: VEL + accel * DT ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh
ps=. (-: width) , 20
pe=. ps + 150 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glclear
glbrush glrgb 91 91 91 NB. gray
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glrect 0 0, width, 20
glbrush glrgb 255 255 0 NB. yellow
glellipse (,~ pe - -:) 15 15 NB. orb
)
pend_run</lang>
Java
<lang java>import java.awt.*; import javax.swing.*;
public class Pendulum extends JPanel implements Runnable {
private double angle = Math.PI / 2; private int length;
public Pendulum(int length) {
this.length = length;
setDoubleBuffered(true);
}
@Override
public void paint(Graphics g) {
g.setColor(Color.WHITE);
g.fillRect(0, 0, getWidth(), getHeight());
g.setColor(Color.BLACK);
int anchorX = getWidth() / 2, anchorY = getHeight() / 4;
int ballX = anchorX + (int) (Math.sin(angle) * length);
int ballY = anchorY + (int) (Math.cos(angle) * length);
g.drawLine(anchorX, anchorY, ballX, ballY);
g.fillOval(anchorX - 3, anchorY - 4, 7, 7);
g.fillOval(ballX - 7, ballY - 7, 14, 14);
}
public void run() {
double angleAccel, angleVelocity = 0, dt = 0.1;
while (true) {
angleAccel = -9.81 / length * Math.sin(angle);
angleVelocity += angleAccel * dt;
angle += angleVelocity * dt;
repaint();
try { Thread.sleep(15); } catch (InterruptedException ex) {}
}
}
@Override
public Dimension getPreferredSize() {
return new Dimension(2 * length + 50, length / 2 * 3);
}
public static void main(String[] args) {
JFrame f = new JFrame("Pendulum");
Pendulum p = new Pendulum(200);
f.add(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setVisible(true);
new Thread(p).start();
}
}</lang>
JavaScript
With <canvas>
(plus gratuitous motion blur)
<lang javascript><html><head>
<title>Pendulum</title>
</head><body style="background: gray;">
<canvas id="canvas" width="600" height="600">
Sorry, your browser does not support the <canvas> used to display the pendulum animation.
</canvas> <script>
function PendulumSim(length_m, gravity_mps2, initialAngle_rad, timestep_ms, callback) {
var velocity = 0;
var angle = initialAngle_rad;
var k = -gravity_mps2/length_m;
var timestep_s = timestep_ms / 1000;
return setInterval(function () {
var acceleration = k * Math.sin(angle);
velocity += acceleration * timestep_s;
angle += velocity * timestep_s;
callback(angle);
}, timestep_ms);
}
var canvas = document.getElementById('canvas');
var context = canvas.getContext('2d');
var prev=0;
var sim = PendulumSim(1, 9.80665, Math.PI*99/100, 10, function (angle) {
var rPend = Math.min(canvas.width, canvas.height) * 0.47;
var rBall = Math.min(canvas.width, canvas.height) * 0.02;
var rBar = Math.min(canvas.width, canvas.height) * 0.005;
var ballX = Math.sin(angle) * rPend;
var ballY = Math.cos(angle) * rPend;
context.fillStyle = "rgba(255,255,255,0.51)"; context.globalCompositeOperation = "destination-out"; context.fillRect(0, 0, canvas.width, canvas.height); context.fillStyle = "yellow"; context.strokeStyle = "rgba(0,0,0,"+Math.max(0,1-Math.abs(prev-angle)*10)+")"; context.globalCompositeOperation = "source-over";
context.save();
context.translate(canvas.width/2, canvas.height/2);
context.rotate(angle);
context.beginPath();
context.rect(-rBar, -rBar, rBar*2, rPend+rBar*2);
context.fill();
context.stroke();
context.beginPath();
context.arc(0, rPend, rBall, 0, Math.PI*2, false);
context.fill();
context.stroke();
context.restore();
prev=angle;
});
</script>
</body></html></lang>
Within SVG
If we use SVG we don't even have to make a HTML document. We can put the script inside SVG.
To do things a bit differently, we'll use a stereographic projection of the circle, in order to get algebraic Euler-Lagrange equations which we'll integrate with the Runge-Kutta method.
Also we'll use a dimensionless formulation of the problem (taking unit value for the mass, the length and so on).
<lang javascript><svg height="100%" width="100%" viewBox="-2 0 4 4">
<line id="string" x1="0" y1="0" x2="1" y2="0" stroke="grey" stroke-width="0.05" /> <circle id="ball" cx="0" cy="0" r="0.1" fill="black" /> <script> /*jshint esnext: true */
function rk4(dt, x, f) {
"use strict"; let indices = [...new Array(x.length).keys()], map = $ => indices.map($), dtx = $ => map( i => $[i]*dt ), a = dtx(f(map(i => x[i]))), b = dtx(f(map(i => x[i] + a[i]/2))), c = dtx(f(map(i => x[i] + b[i]/2))), d = dtx(f(map(i => x[i] + c[i]))); return map(i => (a[i] + 2*b[i] + 2*c[i] + d[i])/6);
}
function M($) {
let $2 = $*$; return [2*$/(1+$2),(1-$2)/(1+$2)];
}
function setPendulumPos(mu) {
const string = document.getElementById("string"),
ball = document.getElementById("ball");
let m = M(mu),
x = m[0],
y = m[1];
string.setAttribute("x2", x);
string.setAttribute("y2", y);
ball.setAttribute("cx", x);
ball.setAttribute("cy", y);
}
var q = [1, 0]; setPendulumPos(q[0]);
var previousTimestamp; function animate(timestamp) {
if (previousTimestamp === undefined) {
previousTimestamp = timestamp;
} else {
let dq = rk4((timestamp - previousTimestamp)/1000, q, $ => [$[1], 2*$[1]*$[1]*$[0]/(1+$[0]*$[0]) - $[0]]);
q = [q[0] + dq[0], q[1] + dq[1]];
setPendulumPos(q[0]);
previousTimestamp = timestamp;
}
window.requestAnimationFrame(animate);
}
window.requestAnimationFrame(animate)
</script>
</svg>
Julia
Differential equation based solution using the Luxor graphics library.<lang julia>using Luxor using Colors using BoundaryValueDiffEq
- constants for differential equations and movie
const g = 9.81 const L = 1.0 # pendulum length in meters const bobd = 0.10 # pendulum bob diameter in meters const framerate = 50.0 # intended frame rate/sec const t0 = 0.0 # start time (s) const tf = 2.3 # end simulation time (s) const dtframe = 1.0/framerate # time increment per frame const tspan = LinRange(t0, tf, Int(floor(tf*framerate))) # array of time points in animation
const bgcolor = "black" # gif background const leaderhue = (0.80, 0.70, 0.20) # gif swing arm hue light gold const hslcolors = [HSL(col) for col in (distinguishable_colors(
Int(floor(tf*framerate)+3),[RGB(1,1,1)])[2:end])]
const giffilename = "pendulum.gif" # output file
- differential equations
simplependulum(du, u, p, t) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ)) bc2(residual, u, p, t) = (residual[1] = u[end÷2][1] + pi/2; residual[2] = u[end][1] - pi/2) bvp2 = BVProblem(simplependulum, bc2, [pi/2,pi/2], (tspan[1],tspan[end])) sol2 = solve(bvp2, MIRK4(), dt=dtframe) # use the MIRK4 solver for TwoPointBVProblem
- movie making background
backdrop(scene, framenumber) = background(bgcolor)
function frame(scene, framenumber)
u1, u2 = sol2.u[framenumber]
y, x = L*cos(u1), L*sin(u1)
sethue(leaderhue)
poly([Point(-4.0, 0.0), Point(4.0, 0.0),
Point(160.0x,160.0y)], :fill)
sethue(Colors.HSV(framenumber*4.0, 1, 1))
circle(Point(160.0x,160.0y), 160bobd, :fill)
text(string("frame $framenumber of $(scene.framerange.stop)"),
Point(0.0, -190.0),
halign=:center)
end
muv = Movie(400, 400, "Pendulum Demo", 1:length(tspan)) animate(muv, [Scene(muv, backdrop),
Scene(muv, frame, easingfunction=easeinoutcubic)],
creategif=true, pathname=giffilename)
</lang>
Kotlin
Conversion of Java snippet. <lang scala>import java.awt.* import java.util.concurrent.* import javax.swing.*
class Pendulum(private val length: Int) : JPanel(), Runnable {
init {
val f = JFrame("Pendulum")
f.add(this)
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.pack()
f.isVisible = true
isDoubleBuffered = true
}
override fun paint(g: Graphics) {
with(g) {
color = Color.WHITE
fillRect(0, 0, width, height)
color = Color.BLACK
val anchor = Element(width / 2, height / 4)
val ball = Element((anchor.x + Math.sin(angle) * length).toInt(), (anchor.y + Math.cos(angle) * length).toInt())
drawLine(anchor.x, anchor.y, ball.x, ball.y)
fillOval(anchor.x - 3, anchor.y - 4, 7, 7)
fillOval(ball.x - 7, ball.y - 7, 14, 14)
}
}
override fun run() {
angleVelocity += -9.81 / length * Math.sin(angle) * dt
angle += angleVelocity * dt
repaint()
}
override fun getPreferredSize() = Dimension(2 * length + 50, length / 2 * 3)
private data class Element(val x: Int, val y: Int)
private val dt = 0.1 private var angle = Math.PI / 2 private var angleVelocity = 0.0
}
fun main(a: Array<String>) {
val executor = Executors.newSingleThreadScheduledExecutor() executor.scheduleAtFixedRate(Pendulum(200), 0, 15, TimeUnit.MILLISECONDS)
}</lang>
Liberty BASIC
<lang lb>nomainwin
WindowWidth = 400 WindowHeight = 300
open "Pendulum" for graphics_nsb_nf as #main #main "down;fill white; flush" #main "color black" #main "trapclose [quit.main]"
Angle = asn(1) DeltaT = 0.1 PendLength = 150 FixX = int(WindowWidth / 2) FixY = 40
timer 30, [swing]
wait
[swing]
#main "cls" #main "discard"
PlumbobX = FixX + int(sin(Angle) * PendLength) PlumbobY = FixY + int(cos(Angle) * PendLength) AngAccel = -9.81 / PendLength * sin(Angle) AngVelocity = AngVelocity + AngAccel * DeltaT Angle = Angle + AngVelocity * DeltaT
#main "backcolor black" #main "place ";FixX;" ";FixY #main "circlefilled 3" #main "line ";FixX;" ";FixY;" ";PlumbobX;" ";PlumbobY #main "backcolor red" #main "circlefilled 10"
wait
[quit.main]
close #main end</lang>
Lingo
<lang Lingo>global RODLEN, GRAVITY, DT global velocity, acceleration, angle, posX, posY
on startMovie
-- window properties _movie.stage.title = "Pendulum" _movie.stage.titlebarOptions.visible = TRUE _movie.stage.rect = rect(0, 0, 400, 400) _movie.centerStage = TRUE _movie.puppetTempo(30) RODLEN = 180 GRAVITY = -9.8 DT = 0.03 velocity = 0.0 acceleration = 0.0 angle = PI/3 posX = 200 - sin(angle) * RODLEN posY = 100 + cos(angle) * RODLEN paint() -- show the window _movie.stage.visible = TRUE
end
on enterFrame
acceleration = GRAVITY * sin(angle) velocity = velocity + acceleration * DT angle = angle + velocity * DT posX = 200 - sin(angle) * rodLen posY = 100 + cos(angle) * rodLen paint()
end
on paint
img = _movie.stage.image img.fill(img.rect, rgb(255,255,255)) img.fill(point(200-5, 100-5), point(200+5, 100+5), [#shapeType:#oval,#color:rgb(0,0,0)]) img.draw(point(200, 100), point(posX, posY), [#color:rgb(0,0,0)]) img.fill(point(posX-20, posY-20), point(posX+20, posY+20), [#shapeType:#oval,#lineSize:1,#bgColor:rgb(0,0,0),#color:rgb(255,255,0)])
end</lang>
Logo
<lang logo>make "angle 45 make "L 1 make "bob 10
to draw.pendulum
clearscreen seth :angle+180 ; down on screen is 180 forward :L*100-:bob penup forward :bob pendown arc 360 :bob
end
make "G 9.80665 make "dt 1/30 make "acc 0 make "vel 0
to step.pendulum
make "acc -:G / :L * sin :angle make "vel :vel + :acc * :dt make "angle :angle + :vel * :dt wait :dt*60 draw.pendulum
end
hideturtle until [key?] [step.pendulum]</lang>
Lua
Needs LÖVE 2D Engine <lang lua> function degToRad( d )
return d * 0.01745329251
end
function love.load()
g = love.graphics rodLen, gravity, velocity, acceleration = 260, 3, 0, 0 halfWid, damp = g.getWidth() / 2, .989 posX, posY, angle = halfWid TWO_PI, angle = math.pi * 2, degToRad( 90 )
end
function love.update( dt )
acceleration = -gravity / rodLen * math.sin( angle ) angle = angle + velocity; if angle > TWO_PI then angle = 0 end velocity = velocity + acceleration velocity = velocity * damp posX = halfWid + math.sin( angle ) * rodLen posY = math.cos( angle ) * rodLen
end
function love.draw()
g.setColor( 250, 0, 250 ) g.circle( "fill", halfWid, 0, 8 ) g.line( halfWid, 4, posX, posY ) g.setColor( 250, 100, 20 ) g.circle( "fill", posX, posY, 20 )
end </lang>
M2000 Interpreter
<lang M2000 Interpreter> Module Pendulum {
back()
degree=180/pi
THETA=Pi/2
SPEED=0
G=9.81
L=0.5
Profiler
lasttimecount=0
cc=40 ' 40 ms every draw
accold=0
Every cc {
ACCEL=G*SIN(THETA*degree)/L/50
SPEED+=ACCEL/cc
THETA+=SPEED
Pendulum(THETA)
if KeyPress(32) Then Exit
}
Sub back()
If not IsWine then Smooth On
Cls 7,0
Pen 0
Move 0, scale.y/4
Draw scale.x,0
Step -scale.x/2
circle fill #AAAAAA, scale.x/50
Hold ' hold this as background
End Sub
Sub Pendulum(x)
x+=pi/2
Release ' place stored background to screen
Width scale.x/2000 {
Draw Angle x, scale.y/2.5
Width 1 {
Circle Fill 14, scale.x/25
}
Step Angle x, -scale.y/2.5
}
Print @(1,1), lasttimecount
if sgn(accold)<>sgn(ACCEL) then lasttimecount=timecount: Profiler
accold=ACCEL
Refresh 1000
End Sub
} Pendulum </lang>
Mathematica / Wolfram Language
<lang Mathematica>freq = 8; length = freq^(-1/2); Animate[Graphics[
List[{Line[{{0, 0}, length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}], PointSize[Large],
Point[{length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}]}],
PlotRange -> {{-0.3, 0.3}, {-0.5, 0}}], {t, 0, 1}, AnimationRate -> 0.07]</lang>
MATLAB
pendulum.m <lang MATLAB>%This is a numerical simulation of a pendulum with a massless pivot arm.
%% User Defined Parameters %Define external parameters g = -9.8; deltaTime = 1/50; %Decreasing this will increase simulation accuracy endTime = 16;
%Define pendulum rodPivotPoint = [2 2]; %rectangular coordinates rodLength = 1; mass = 1; %of the bob radius = .2; %of the bob theta = 45; %degrees, defines initial position of the bob velocity = [0 0]; %cylindrical coordinates; first entry is radial velocity,
%second entry is angular velocity
%% Simulation assert(radius < rodLength,'Pendulum bob radius must be less than the length of the rod.');
position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]); %in rectangular coordinates
%Generate graphics, render pendulum figure; axesHandle = gca; xlim(axesHandle, [(rodPivotPoint(1) - rodLength - radius) (rodPivotPoint(1) + rodLength + radius)] ); ylim(axesHandle, [(rodPivotPoint(2) - rodLength - radius) (rodPivotPoint(2) + rodLength + radius)] );
rectHandle = rectangle('Position',[(position - radius/2) radius radius],...
'Curvature',[1,1],'FaceColor','g'); %Pendulum bob
hold on plot(rodPivotPoint(1),rodPivotPoint(2),'^'); %pendulum pivot lineHandle = line([rodPivotPoint(1) position(1)],...
[rodPivotPoint(2) position(2)]); %pendulum rod
hold off
%Run simulation, all calculations are performed in cylindrical coordinates for time = (deltaTime:deltaTime:endTime)
drawnow; %Forces MATLAB to render the pendulum
%Find total force
gravitationalForceCylindrical = [mass*g*cosd(theta) mass*g*sind(theta)];
%This code is just incase you want to add more forces,e.g friction
totalForce = gravitationalForceCylindrical;
%If the rod isn't massless or is a spring, etc., modify this line
%accordingly
rodForce = [-totalForce(1) 0]; %cylindrical coordinates
totalForce = totalForce + rodForce;
acceleration = totalForce / mass; %F = ma
velocity = velocity + acceleration * deltaTime;
rodLength = rodLength + velocity(1) * deltaTime;
theta = theta + velocity(2) * deltaTime; % Attention!! Mistake here.
% Velocity needs to be divided by pendulum length and scaled to degrees:
% theta = theta + velocity(2) * deltaTime/rodLength/pi*180;
position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]);
%Update figure with new position info
set(rectHandle,'Position',[(position - radius/2) radius radius]);
set(lineHandle,'XData',[rodPivotPoint(1) position(1)],'YData',...
[rodPivotPoint(2) position(2)]);
end</lang>
Nim
OpenGL version
Conversion from C with some modifications: changing some variable names, adding a display function to make the program work with "freeGlut", choosing another initial angle, etc.
<lang Nim># Pendulum simulation.
import math import times
import opengl import opengl/glut
var
# Simulation variables. lg: float # Pendulum length. g: float # Gravity (should be positive). currTime: Time # Current time. theta0: float # Initial angle. theta: float # Current angle. omega: float # Angular velocity = derivative of theta. accel: float # Angular acceleration = derivative of omega. e: float # Total energy.
- ---------------------------------------------------------------------------------------------------
proc initSimulation(length, gravitation, start: float) =
## Initialize the simulation.
lg = length g = gravitation currTime = getTime() theta0 = start # Initial angle for which omega = 0. theta = start omega = 0 accel = -g / lg * sin(theta0) e = g * lg * (1 - cos(theta0)) # Total energy = potential energy when starting.
- ---------------------------------------------------------------------------------------------------
proc elapsed(): float =
## Return the elapsed time since previous call, expressed in seconds.
let nextTime = getTime() result = (nextTime - currTime).inMicroseconds.float / 1e6 currTime = nextTime
- ---------------------------------------------------------------------------------------------------
proc resize(w, h: GLsizei) =
## Resize the window.
glViewport(0, 0, w, h) glMatrixMode(GL_PROJECTION) glLoadIdentity()
glMatrixMode(GL_MODELVIEW) glLoadIdentity() glOrtho(0, GLdouble(w), GLdouble(h), 0, -1, 1)
- ---------------------------------------------------------------------------------------------------
proc render() {.cdecl.} =
## Render the window.
# Compute the position of the mass. var x = 320 + 300 * sin(theta) var y = 300 * cos(theta)
resize(640, 320) glClear(GL_COLOR_BUFFER_BIT)
# Draw the line from pivot to mass. glBegin(GL_LINES) glVertex2d(320, 0) glVertex2d(x, y) glEnd() glFlush()
# Update theta and omega. let dt = elapsed() theta += (omega + dt * accel / 2) * dt omega += accel * dt
# If, due to computation errors, potential energy is greater than total energy, # reset theta to ±theta0 and omega to 0. if lg * g * (1 - cos(theta)) >= e: theta = sgn(theta).toFloat * theta0 omega = 0
accel = -g / lg * sin(theta)
- ---------------------------------------------------------------------------------------------------
proc initGfx(argc: ptr cint; argv: pointer) =
## Initialize OpenGL rendering.
glutInit(argc, argv)
glutInitDisplayMode(GLUT_RGB)
glutInitWindowSize(640, 320)
glutIdleFunc(render)
discard glutCreateWindow("Pendulum")
glutDisplayFunc(render)
loadExtensions()
- ———————————————————————————————————————————————————————————————————————————————————————————————————
initSimulation(length = 5, gravitation = 9.81, start = PI / 3)
var argc: cint = 0 initGfx(addr(argc), nil) glutMainLoop()</lang>
Gtk3 version
This version uses the same equations but replace OpenGL by Gtk3 with the “gintro” bindings.
<lang Nim># Pendulum simulation.
import math import times
import gintro/[gobject, gdk, gtk, gio, cairo] import gintro/glib except Pi
type
# Description of the simulation. Simulation = ref object area: DrawingArea # Drawing area. length: float # Pendulum length. g: float # Gravity (should be positive). time: Time # Current time. theta0: float # initial angle. theta: float # Current angle. omega: float # Angular velocity = derivative of theta. accel: float # Angular acceleration = derivative of omega. e: float # Total energy.
- ---------------------------------------------------------------------------------------------------
proc newSimulation(area: DrawingArea; length, g, theta0: float): Simulation {.noInit.} =
## Allocate and initialize the simulation object.
new(result) result.area = area result.length = length result.g = g result.time = getTime() result.theta0 = theta0 result.theta = theta0 result.omega = 0 result.accel = -g / length * sin(theta0) result.e = g * length * (1 - cos(theta0)) # Total energy = potential energy when starting.
- ---------------------------------------------------------------------------------------------------
template toFloat(dt: Duration): float = dt.inNanoseconds.float / 1e9
- ---------------------------------------------------------------------------------------------------
const Origin = (x: 320.0, y: 100.0) # Pivot coordinates. const Scale = 300 # Coordinates scaling constant.
proc draw(sim: Simulation; context: cairo.Context) =
## Draw the pendulum.
# Compute coordinates in drawing area. let x = Origin.x + sin(sim.theta) * Scale let y = Origin.y + cos(sim.theta) * Scale
# Clear the region. context.moveTo(0, 0) context.setSource(0.0, 0.0, 0.0) context.paint()
# Draw pendulum. context.moveTo(Origin.x, Origin.y) context.setSource(0.3, 1.0, 0.3) context.lineTo(x, y) context.stroke()
# Draw pivot. context.setSource(0.3, 0.3, 1.0) context.arc(Origin.x, Origin.y, 8, 0, 2 * Pi) context.fill()
# Draw mass. context.setSource(1.0, 0.3, 0.3) context.arc(x, y, 8, 0, 2 * Pi) context.fill()
- ---------------------------------------------------------------------------------------------------
proc update(sim: Simulation): gboolean =
## Update the simulation state.
# compute time interval. let nextTime = getTime() let dt = (nextTime - sim.time).toFloat sim.time = nextTime
# Update theta and omega. sim.theta += (sim.omega + dt * sim.accel / 2) * dt sim.omega += sim.accel * dt
# If, due to computation errors, potential energy is greater than total energy, # reset theta to ±theta0 and omega to 0. if sim.length * sim.g * (1 - cos(sim.theta)) >= sim.e: sim.theta = sgn(sim.theta).toFloat * sim.theta0 sim.omega = 0
# Compute acceleration. sim.accel = -sim.g / sim.length * sin(sim.theta)
result = gboolean(1)
sim.draw(sim.area.window.cairoCreate())
- ---------------------------------------------------------------------------------------------------
proc activate(app: Application) =
## Activate the application.
let window = app.newApplicationWindow()
window.setSizeRequest(640, 480)
window.setTitle("Pendulum simulation")
let area = newDrawingArea() window.add(area)
let sim = newSimulation(area, length = 5, g = 9.81, theta0 = PI / 3)
timeoutAdd(10, update, sim)
window.showAll()
- ———————————————————————————————————————————————————————————————————————————————————————————————————
let app = newApplication(Application, "Rosetta.pendulum") discard app.connect("activate", activate) discard app.run()</lang>
ooRexx
ooRexx does not have a portable GUI, but this version is similar to the Ada version and just prints out the coordinates of the end of the pendulum. <lang ooRexx> pendulum = .pendulum~new(10, 30)
before = .datetime~new do 100 -- somewhat arbitrary loop count
call syssleep .2 now = .datetime~new pendulum~update(now - before) before = now say " X:" pendulum~x " Y:" pendulum~y
end
- class pendulum
- method init
expose length theta x y velocity use arg length, theta x = rxcalcsin(theta) * length y = rxcalccos(theta) * length velocity = 0
- attribute x GET
- attribute y GET
- constant g -9.81 -- acceleration due to gravity
- method update
expose length theta x y velocity use arg duration acceleration = self~g / length * rxcalcsin(theta) durationSeconds = duration~microseconds / 1000000 x = rxcalcsin(theta, length) y = rxcalccos(theta, length) velocity = velocity + acceleration * durationSeconds theta = theta + velocity * durationSeconds
- requires rxmath library
</lang>
Oz
Inspired by the E and Ruby versions.
<lang oz>declare
[QTk] = {Link ['x-oz://system/wp/QTk.ozf']}
Pi = 3.14159265
class PendulumModel
feat
K
attr
angle velocity
meth init(length:L <= 1.0 %% meters
gravity:G <= 9.81 %% m/s² initialAngle:A <= Pi/2.) %% radians self.K = ~G / L angle := A velocity := 0.0
end
meth nextAngle(deltaT:DeltaTMS %% milliseconds
?Angle) %% radians
DeltaT = {Int.toFloat DeltaTMS} / 1000.0 %% seconds
Acceleration = self.K * {Sin @angle}
in
velocity := @velocity + Acceleration * DeltaT
angle := @angle + @velocity * DeltaT
Angle = @angle
end
end
%% Animates a pendulum on a given canvas.
class PendulumAnimation from Time.repeat
feat
Pend
Rod
Bob
home:pos(x:160 y:50)
length:140.0
delay
meth init(Pendulum Canvas delay:Delay <= 25) %% milliseconds
self.Pend = Pendulum self.delay = Delay %% plate and pivot
{Canvas create(line 0 self.home.y 320 self.home.y width:2 fill:grey50)}
{Canvas create(oval 155 self.home.y-5 165 self.home.y+5 fill:grey50 outline:black)}
%% the pendulum itself self.Rod = {Canvas create(line 1 1 1 1 width:3 fill:black handle:$)}
self.Bob = {Canvas create(oval 1 1 2 2 fill:yellow outline:black handle:$)}
%%
{self setRepAll(action:Animate delay:Delay)}
end
meth Animate
Theta = {self.Pend nextAngle(deltaT:self.delay $)} %% calculate x and y from angle X = self.home.x + {Float.toInt self.length * {Sin Theta}} Y = self.home.y + {Float.toInt self.length * {Cos Theta}}
in
%% update canvas try {self.Rod setCoords(self.home.x self.home.y X Y)} {self.Bob setCoords(X-15 Y-15 X+15 Y+15)} catch system(tk(alreadyClosed ...) ...) then skip end
end
end
Pendulum = {New PendulumModel init}
Canvas
GUI = td(title:"Pendulum"
canvas(width:320 height:210 handle:?Canvas)
action:proc {$} {Animation stop} {Window close} end
)
Window = {QTk.build GUI}
Animation = {New PendulumAnimation init(Pendulum Canvas)}
in
{Window show}
{Animation go}
</lang>
Perl
This does not have the window resizing handling that Tcl does.
<lang perl> use strict; use warnings; use Tk; use Math::Trig qw/:pi/;
my $root = new MainWindow( -title => 'Pendulum Animation' ); my $canvas = $root->Canvas(-width => 320, -height => 200); my $after_id;
for ($canvas) { $_->createLine( 0, 25, 320, 25, -tags => [qw/plate/], -width => 2, -fill => 'grey50' ); $_->createOval( 155, 20, 165, 30, -tags => [qw/pivot outline/], -fill => 'grey50' ); $_->createLine( 1, 1, 1, 1, -tags => [qw/rod width/], -width => 3, -fill => 'black' ); $_->createOval( 1, 1, 2, 2, -tags => [qw/bob outline/], -fill => 'yellow' ); }
$canvas->raise('pivot'); $canvas->pack(-fill => 'both', -expand => 1); my ($Theta, $dTheta, $length, $homeX, $homeY) = (45, 0, 150, 160, 25);
sub show_pendulum {
my $angle = $Theta * pi() / 180;
my $x = $homeX + $length * sin($angle);
my $y = $homeY + $length * cos($angle);
$canvas->coords('rod', $homeX, $homeY, $x, $y);
$canvas->coords('bob', $x-15, $y-15, $x+15, $y+15);
}
sub recompute_angle {
my $scaling = 3000.0 / ($length ** 2); # first estimate my $firstDDTheta = -sin($Theta * pi / 180) * $scaling; my $midDTheta = $dTheta + $firstDDTheta; my $midTheta = $Theta + ($dTheta + $midDTheta)/2; # second estimate my $midDDTheta = -sin($midTheta * pi/ 180) * $scaling; $midDTheta = $dTheta + ($firstDDTheta + $midDDTheta)/2; $midTheta = $Theta + ($dTheta + $midDTheta)/2; # again, first $midDDTheta = -sin($midTheta * pi/ 180) * $scaling; my $lastDTheta = $midDTheta + $midDDTheta; my $lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2; # again, second my $lastDDTheta = -sin($lastTheta * pi/180) * $scaling; $lastDTheta = $midDTheta + ($midDDTheta + $lastDDTheta)/2; $lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2; # Now put the values back in our globals $dTheta = $lastDTheta; $Theta = $lastTheta;
}
sub animate {
recompute_angle;
show_pendulum;
$after_id = $root->after(15 => sub {animate() });
}
show_pendulum; $after_id = $root->after(500 => sub {animate});
$canvas->bind('<Destroy>' => sub {$after_id->cancel}); MainLoop;</lang>
Phix
You can run this online here.
-- -- demo\rosetta\animate_pendulum.exw -- ================================= -- -- Author Pete Lomax, March 2017 -- -- Port of animate_pendulum.exw from arwen to pGUI, which is now -- preserved as a comment below (in the distro version only). -- -- With help from lesterb, updates now in timer_cb not redraw_cb, -- variables better named, and velocity problem sorted, July 2018. -- constant full = false -- set true for full swing to near-vertical. -- false performs swing to horizontal only. -- (adjusts the starting angle, pivot point, -- and canvas size, only.) include pGUI.e Ihandle dlg, canvas, timer cdCanvas cdcanvas constant g = 50 atom angle = iff(full?PI-0.01:PI/2), -- (near_vertical | horiz) velocity = 0 integer w = 0, h = 0, len = 0 function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/) {w, h} = IupGetIntInt(canvas, "DRAWSIZE") cdCanvasActivate(cdcanvas) cdCanvasClear(cdcanvas) -- new suspension point: integer sX = floor(w/2) integer sY = floor(h/iff(full?2:16)) -- (mid | top) -- repaint: integer eX = floor(len*sin(angle)+sX) integer eY = floor(len*cos(angle)+sY) cdCanvasSetForeground(cdcanvas, CD_CYAN) cdCanvasLine(cdcanvas, sX, h-sY, eX, h-eY) cdCanvasSetForeground(cdcanvas, CD_DARK_GREEN) cdCanvasSector(cdcanvas, sX, h-sY, 5, 5, 0, 360) cdCanvasSetForeground(cdcanvas, CD_BLUE) cdCanvasSector(cdcanvas, eX, h-eY, 35, 35, 0, 360) cdCanvasFlush(cdcanvas) return IUP_DEFAULT end function function timer_cb(Ihandle /*ih*/) if w!=0 then integer newlen = floor(w/2)-30 if newlen!=len then len = newlen atom tmp = 2*g*len*(cos(angle)) velocity = iff(tmp<0?0:sqrt(tmp)*sign(velocity)) end if atom dt = 0.2/w atom acceleration = -len*sin(angle)*g velocity += dt*acceleration angle += dt*velocity IupUpdate(canvas) end if return IUP_IGNORE end function function map_cb(Ihandle ih) atom res = IupGetDouble(NULL, "SCREENDPI")/25.4 IupGLMakeCurrent(canvas) if platform()=JS then cdcanvas = cdCreateCanvas(CD_IUP, canvas) else cdcanvas = cdCreateCanvas(CD_GL, "10x10 %g", {res}) end if cdCanvasSetBackground(cdcanvas, CD_PARCHMENT) return IUP_DEFAULT end function function canvas_resize_cb(Ihandle /*canvas*/) integer {canvas_width, canvas_height} = IupGetIntInt(canvas, "DRAWSIZE") atom res = IupGetDouble(NULL, "SCREENDPI")/25.4 cdCanvasSetAttribute(cdcanvas, "SIZE", "%dx%d %g", {canvas_width, canvas_height, res}) return IUP_DEFAULT end function procedure main() IupOpen() canvas = IupGLCanvas() IupSetAttribute(canvas, "RASTERSIZE", iff(full?"640x640":"640x340")) -- (fit 360|180) IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb")) IupSetCallback(canvas, "RESIZE_CB", Icallback("canvas_resize_cb")) timer = IupTimer(Icallback("timer_cb"), 20) dlg = IupDialog(canvas) IupSetAttribute(dlg, "TITLE", "Animated Pendulum") IupShow(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
PicoLisp
A minimalist solution. The pendulum consists of the center point '+', and the swinging xterm cursor. <lang PicoLisp>(load "@lib/math.l")
(de pendulum (X Y Len)
(let (Angle pi/2 V 0)
(call 'clear)
(call 'tput "cup" Y X)
(prin '+)
(call 'tput "cup" 1 (+ X Len))
(until (key 25) # 25 ms
(let A (*/ (sin Angle) -9.81 1.0)
(inc 'V (*/ A 40)) # DT = 25 ms = 1/40 sec
(inc 'Angle (*/ V 40)) )
(call 'tput "cup"
(+ Y (*/ Len (cos Angle) 2.2)) # Compensate for aspect ratio
(+ X (*/ Len (sin Angle) 1.0)) ) ) ) )</lang>
Test (hit any key to stop): <lang PicoLisp>(pendulum 40 1 36)</lang>
Prolog
SWI-Prolog has a graphic interface XPCE. <lang Prolog>:- use_module(library(pce)).
pendulum :- new(D, window('Pendulum')), send(D, size, size(560, 300)), new(Line, line(80, 50, 480, 50)), send(D, display, Line), new(Circle, circle(20)), send(Circle, fill_pattern, colour(@default, 0, 0, 0)), new(Boule, circle(60)), send(Boule, fill_pattern, colour(@default, 0, 0, 0)), send(D, display, Circle, point(270,40)), send(Circle, handle, handle(h/2, w/2, in)), send(Boule, handle, handle(h/2, w/2, out)), send(Circle, connect, Boule, link(in, out, line(0,0,0,0,none))), new(Anim, animation(D, 0.0, Boule, 200.0)), send(D, done_message, and(message(Anim, free), message(Boule, free), message(Circle, free), message(@receiver,destroy))), send(Anim?mytimer, start), send(D, open).
- - pce_begin_class(animation(window, angle, boule, len_pendulum), object).
variable(window, object, both, "Display window"). variable(boule, object, both, "bowl of the pendulum"). variable(len_pendulum, object, both, "len of the pendulum"). variable(angle, object, both, "angle with the horizontal"). variable(delta, object, both, "increment of the angle"). variable(mytimer, timer, both, "timer of the animation").
initialise(P, W:object, A:object, B : object, L:object) :->
"Creation of the object"::
send(P, window, W),
send(P, angle, A),
send(P, boule, B),
send(P, len_pendulum, L),
send(P, delta, 0.01),
send(P, mytimer, new(_, timer(0.01,message(P, anim_message)))).
% method called when the object is destroyed % first the timer is stopped % then all the resources are freed unlink(P) :-> send(P?mytimer, stop), send(P, send_super, unlink).
% message processed by the timer
anim_message(P) :->
get(P, angle, A),
get(P, len_pendulum, L),
calc(A, L, X, Y),
get(P, window, W),
get(P, boule, B),
send(W, display, B, point(X,Y)),
% computation of the next position
get(P, delta, D),
next_Angle(A, D, NA, ND),
send(P, angle, NA),
send(P, delta, ND).
- - pce_end_class.
% computation of the position of the bowl. calc(Ang, Len, X, Y) :- X is Len * cos(Ang)+ 250, Y is Len * sin(Ang) + 20.
% computation of the next angle
% if we reach 0 or pi, delta change.
next_Angle(A, D, NA, ND) :-
NA is D + A,
(((D > 0, abs(pi-NA) < 0.01); (D < 0, abs(NA) < 0.01))->
ND = - D;
ND = D).
</lang>
PureBasic
If the code was part of a larger application it could be improved by specifying constants for the locations of image elements. <lang PureBasic>Procedure handleError(x, msg.s)
If Not x
MessageRequester("Error", msg)
End
EndIf
EndProcedure
- ScreenW = 320
- ScreenH = 210
handleError(OpenWindow(0, 0, 0, #ScreenW, #ScreenH, "Animated Pendulum", #PB_Window_SystemMenu), "Can't open window.") handleError(InitSprite(), "Can't setup sprite display.") handleError(OpenWindowedScreen(WindowID(0), 0, 0, #ScreenW, #ScreenH, 0, 0, 0), "Can't open screen.")
Enumeration ;sprites
#bob_spr #ceiling_spr #pivot_spr
EndEnumeration
TransparentSpriteColor(#PB_Default, RGB(255, 0, 255)) CreateSprite(#bob_spr, 32, 32) StartDrawing(SpriteOutput(#bob_spr))
Box(0, 0, 32, 32, RGB(255, 0, 255)) Circle(16, 16, 15, RGB(253, 252, 3)) DrawingMode(#PB_2DDrawing_Outlined) Circle(16, 16, 15, RGB(0, 0, 0))
StopDrawing()
CreateSprite(#pivot_spr, 10, 10) StartDrawing(SpriteOutput(#pivot_spr))
Box(0, 0, 10, 10, RGB(255, 0, 255)) Circle(5, 5, 4, RGB(125, 125, 125)) DrawingMode(#PB_2DDrawing_Outlined) Circle(5, 5, 4, RGB(0,0 , 0))
StopDrawing()
CreateSprite(#ceiling_spr,#ScreenW,2) StartDrawing(SpriteOutput(#ceiling_spr))
Box(0,0,SpriteWidth(#ceiling_spr), SpriteHeight(#ceiling_spr), RGB(126, 126, 126))
StopDrawing()
Structure pendulum
length.d ; meters constant.d ; -g/l gravity.d ; m/s² angle.d ; radians velocity.d ; m/s
EndStructure
Procedure initPendulum(*pendulum.pendulum, length.d = 1.0, gravity.d = 9.81, initialAngle.d = #PI / 2)
With *pendulum \length = length \gravity = gravity \angle = initialAngle \constant = -gravity / length \velocity = 0.0 EndWith
EndProcedure
Procedure updatePendulum(*pendulum.pendulum, deltaTime.d)
deltaTime = deltaTime / 1000.0 ;ms Protected acceleration.d = *pendulum\constant * Sin(*pendulum\angle) *pendulum\velocity + acceleration * deltaTime *pendulum\angle + *pendulum\velocity * deltaTime
EndProcedure
Procedure drawBackground()
ClearScreen(RGB(190,190,190)) ;draw ceiling DisplaySprite(#ceiling_spr, 0, 47) ;draw pivot DisplayTransparentSprite(#pivot_spr, 154,43) ;origin in upper-left
EndProcedure
Procedure drawPendulum(*pendulum.pendulum)
;draw rod Protected x = *pendulum\length * 140 * Sin(*pendulum\angle) ;scale = 1 m/140 pixels Protected y = *pendulum\length * 140 * Cos(*pendulum\angle) StartDrawing(ScreenOutput()) LineXY(154 + 5,43 + 5, 154 + 5 + x, 43 + 5 + y) ;draw from pivot-center to bob-center, adjusting for origins StopDrawing() ;draw bob DisplayTransparentSprite(#bob_spr, 154 + 5 - 16 + x, 43 + 5 - 16 + y) ;adj for origin in upper-left
EndProcedure
Define pendulum.pendulum, event initPendulum(pendulum) drawPendulum(pendulum)
AddWindowTimer(0, 1, 50) Repeat
event = WindowEvent()
Select event
Case #pb_event_timer
drawBackground()
Select EventTimer()
Case 1
updatePendulum(pendulum, 50)
drawPendulum(pendulum)
EndSelect
FlipBuffers()
Case #PB_Event_CloseWindow
Break
EndSelect
ForEver</lang>
Python
<lang python>import pygame, sys from pygame.locals import * from math import sin, cos, radians
pygame.init()
WINDOWSIZE = 250 TIMETICK = 100 BOBSIZE = 15
window = pygame.display.set_mode((WINDOWSIZE, WINDOWSIZE)) pygame.display.set_caption("Pendulum")
screen = pygame.display.get_surface() screen.fill((255,255,255))
PIVOT = (WINDOWSIZE/2, WINDOWSIZE/10) SWINGLENGTH = PIVOT[1]*4
class BobMass(pygame.sprite.Sprite):
def __init__(self):
pygame.sprite.Sprite.__init__(self)
self.theta = 45
self.dtheta = 0
self.rect = pygame.Rect(PIVOT[0]-SWINGLENGTH*cos(radians(self.theta)),
PIVOT[1]+SWINGLENGTH*sin(radians(self.theta)),
1,1)
self.draw()
def recomputeAngle(self):
scaling = 3000.0/(SWINGLENGTH**2)
firstDDtheta = -sin(radians(self.theta))*scaling
midDtheta = self.dtheta + firstDDtheta
midtheta = self.theta + (self.dtheta + midDtheta)/2.0
midDDtheta = -sin(radians(midtheta))*scaling
midDtheta = self.dtheta + (firstDDtheta + midDDtheta)/2
midtheta = self.theta + (self.dtheta + midDtheta)/2
midDDtheta = -sin(radians(midtheta)) * scaling
lastDtheta = midDtheta + midDDtheta
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
lastDDtheta = -sin(radians(lasttheta)) * scaling
lastDtheta = midDtheta + (midDDtheta + lastDDtheta)/2.0
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
self.dtheta = lastDtheta
self.theta = lasttheta
self.rect = pygame.Rect(PIVOT[0]-
SWINGLENGTH*sin(radians(self.theta)),
PIVOT[1]+
SWINGLENGTH*cos(radians(self.theta)),1,1)
def draw(self):
pygame.draw.circle(screen, (0,0,0), PIVOT, 5, 0)
pygame.draw.circle(screen, (0,0,0), self.rect.center, BOBSIZE, 0)
pygame.draw.aaline(screen, (0,0,0), PIVOT, self.rect.center)
pygame.draw.line(screen, (0,0,0), (0, PIVOT[1]), (WINDOWSIZE, PIVOT[1]))
def update(self):
self.recomputeAngle()
screen.fill((255,255,255))
self.draw()
bob = BobMass()
TICK = USEREVENT + 2 pygame.time.set_timer(TICK, TIMETICK)
def input(events):
for event in events:
if event.type == QUIT:
sys.exit(0)
elif event.type == TICK:
bob.update()
while True:
input(pygame.event.get()) pygame.display.flip()</lang>
Python: using tkinter
<lang python> Python 3.6.5 code using Tkinter graphical user interface.
from tkinter import * import math
class Animation:
def __init__(self, gw):
self.window = gw
self.xoff, self.yoff = 300, 100
self.angle = 0
self.sina = math.sin(self.angle)
self.cosa = math.cos(self.angle)
self.rodhyp = 170
self.bobr = 30
self.bobhyp = self.rodhyp + self.bobr
self.rodx0, self.rody0 = self.xoff, self.yoff
self.ra = self.rodx0
self.rb = self.rody0
self.rc = self.xoff + self.rodhyp*self.sina
self.rd = self.yoff + self.rodhyp*self.cosa
self.ba = self.xoff - self.bobr + self.bobhyp*self.sina
self.bb = self.yoff - self.bobr + self.bobhyp*self.cosa
self.bc = self.xoff + self.bobr + self.bobhyp*self.sina
self.bd = self.yoff + self.bobr + self.bobhyp*self.cosa
self.da = math.pi / 360
# create / fill canvas:
self.cnv = Canvas(gw, bg='lemon chiffon')
self.cnv.pack(fill=BOTH, expand=True)
self.cnv.create_line(0, 100, 600, 100,
fill='dodger blue',
width=3)
radius = 8
self.cnv.create_oval(300-radius, 100-radius,
300+radius, 100+radius,
fill='navy')
self.bob = self.cnv.create_oval(self.ba,
self.bb,
self.bc,
self.bd,
fill='red',
width=2)
self.rod = self.cnv.create_line(self.ra,
self.rb,
self.rc,
self.rd,
fill='dodger blue',
width=6)
self.animate()
def animate(self):
if abs(self.angle) > math.pi / 2:
self.da = - self.da
self.angle += self.da
self.sina = math.sin(self.angle)
self.cosa = math.cos(self.angle)
self.ra = self.rodx0
self.rb = self.rody0
self.rc = self.xoff + self.rodhyp*self.sina
self.rd = self.yoff + self.rodhyp*self.cosa
self.ba = self.xoff - self.bobr + self.bobhyp*self.sina
self.bb = self.yoff - self.bobr + self.bobhyp*self.cosa
self.bc = self.xoff + self.bobr + self.bobhyp*self.sina
self.bd = self.yoff + self.bobr + self.bobhyp*self.cosa
self.cnv.coords(self.rod,
self.ra,
self.rb,
self.rc,
self.rd)
self.cnv.coords(self.bob,
self.ba,
self.bb,
self.bc,
self.bd)
self.window.update()
self.cnv.after(5, self.animate)
root = Tk() root.title('Pendulum') root.geometry('600x400+100+50') root.resizable(False, False) a = Animation(root) root.mainloop() </lang>
QB64
<lang qbasic>'declare and initialize variables CONST PI = 3.141592
DIM SHARED Bob_X, Bob_Y, Pivot_X, Pivot_Y, Rod_Length, Rod_Angle, Bob_Angular_Acceleration, Bob_Angular_Velocity, Delta_Time, Drawing_Scale, G AS DOUBLE DIM SHARED exit_flag AS INTEGER
'set gravity to Earth's by default (in m/s squared) G = -9.80665
'set the pivot at the screen center near the top. Positions are in meters not pixels, and they translate to 320 and 60 pixels Pivot_X = 1.6 Pivot_Y = 0.3
'set the rod length, 0.994 meters by default (gives 1 second period in Earth gravity) Rod_Length = 0.994 'set the initial rod angle to 6 degrees and convert to radians. 6 degrees seems small but it is near to what clocks use so it 'makes the pendulum look like a clock's. More amplitude works perfectly but looks silly. Rod_Angle = 6 * (PI / 180) 'set delta time, seconds. 5 miliseconds is precise enough. Delta_Time = 0.05
'because the positions are calculated in meters, the pendulum as drawn would be way too small (1 meter = 1 pixel), 'so a scale factor is introduced (1 meter = 200 pixels by default) Drawing_Scale = 200
'initialize the screen to 640 x 480, 16 colors SCREEN 12
'main loop DO
'math to figure out what the pendulum is doing based on the initial conditions.
'first calculate the position of the bob's center based on the rod angle by using the sine and cosine functions for x and y coordinates Bob_X = (Pivot_X + SIN(Rod_Angle) * Rod_Length) Bob_Y = (Pivot_Y + COS(Rod_Angle) * Rod_Length) 'then based on the rod's last angle, length, and gravitational acceleration, calculate the angular acceleration Bob_Angular_Acceleration = G / Rod_Length * SIN(Rod_Angle) 'integrate the angular acceleration over time to obtain angular velocity Bob_Angular_Velocity = Bob_Angular_Velocity + (Bob_Angular_Acceleration * Delta_Time) 'integrate the angular velocity over time to obtain a new angle for the rod Rod_Angle = Rod_Angle + (Bob_Angular_Velocity * Delta_Time)
'draw the user interface and pendulum position
'clear the screen before drawing the next frame of the animation CLS
'print information PRINT " Gravity: " + STR$(ABS(G)) + " m/sý, Rod Length: " + STR$(Rod_Length); " m" LOCATE 25, 1 PRINT "+/- keys control rod length, numbers 1-5 select gravity, (1 Earth, 2 the Moon, 3 Mars, 4 more 5 less), Q to exit"
'draw the pivot CIRCLE (Pivot_X * Drawing_Scale, Pivot_Y * Drawing_Scale), 5, 8 PAINT STEP(0, 0), 8, 8
'draw the bob CIRCLE (Bob_X * Drawing_Scale, Bob_Y * Drawing_Scale), 20, 14 PAINT STEP(0, 0), 14, 14
'draw the rod LINE (Pivot_X * Drawing_Scale, Pivot_Y * Drawing_Scale)-(Bob_X * Drawing_Scale, Bob_Y * Drawing_Scale), 14
'process input
SELECT CASE UCASE$(INKEY$)
CASE "+"
'lengthen rod
Rod_Length = Rod_Length + 0.01
CASE "-"
'shorten rod
Rod_Length = Rod_Length - 0.01
CASE "1"
'Earth G
G = -9.80665
CASE "2"
'Moon G
G = -1.62
CASE "3"
'Mars G
G = -3.721
CASE "4"
'More G
G = G + 0.1
CASE "5"
'Less G
G = G - 0.1
CASE "Q"
'exit on any other key
exit_flag = 1
END SELECT
'wait before drawing the next frame _DELAY Delta_Time
'loop the animation until the user presses any key
LOOP UNTIL exit_flag = 1</lang>
R
<lang R>library(DescTools)
pendulum<-function(length=5,radius=1,circle.color="white",bg.color="white"){
tseq = c(seq(0,pi,by=.1),seq(pi,0,by=-.1))
slow=.27;fast=.07
sseq = c(seq(slow,fast,length.out = length(tseq)/4),seq(fast,slow,length.out = length(tseq)/4),seq(slow,fast,length.out = length(tseq)/4),seq(fast,slow,length.out = length(tseq)/4))
plot(0,0,xlim=c((-length-radius)*1.2,(length+radius)*1.2),ylim=c((-length-radius)*1.2,0),xaxt="n",yaxt="n",xlab="",ylab="")
cat("Press Esc to end animation")
while(T){
for(i in 1:length(tseq)){
rect(par("usr")[1],par("usr")[3],par("usr")[2],par("usr")[4],col = bg.color)
abline(h=0,col="grey")
points(0,0)
DrawCircle((radius+length)*cos(tseq[i]),(radius+length)*-sin(tseq[i]),r.out=radius,col=circle.color)
lines(c(0,length*cos(tseq[i])),c(0,length*-sin(tseq[i])))
Sys.sleep(sseq[i])
}
}
}
pendulum(5,1,"gold","lightblue")</lang>
Racket
<lang racket>
- lang racket
(require 2htdp/image 2htdp/universe)
(define (pendulum)
(define (accel θ) (- (sin θ)))
(define θ (/ pi 2.5))
(define θ′ 0)
(define θ′′ (accel (/ pi 2.5)))
(define (x θ) (+ 200 (* 150 (sin θ))))
(define (y θ) (* 150 (cos θ)))
(λ (n)
(define p-image (underlay/xy (add-line (empty-scene 400 200) 200 0 (x θ) (y θ) "black")
(- (x θ) 5) (- (y θ) 5) (circle 5 "solid" "blue")))
(set! θ (+ θ (* θ′ 0.04)))
(set! θ′ (+ θ′ (* (accel θ) 0.04)))
p-image))
(animate (pendulum)) </lang>
Raku
(formerly Perl 6)
Handles window resizing, modifies pendulum length and period as window height changes. May need to tweek $ppi scaling to get good looking animation.
<lang perl6>use SDL2::Raw; use Cairo;
my $width = 1000; my $height = 400;
SDL_Init(VIDEO);
my $window = SDL_CreateWindow(
'Pendulum - Raku', SDL_WINDOWPOS_CENTERED_MASK, SDL_WINDOWPOS_CENTERED_MASK, $width, $height, RESIZABLE
);
my $render = SDL_CreateRenderer($window, -1, ACCELERATED +| PRESENTVSYNC);
my $bob = Cairo::Image.create( Cairo::FORMAT_ARGB32, 32, 32 ); given Cairo::Context.new($bob) {
my Cairo::Pattern::Gradient::Radial $sphere .=
create(13.3, 12.8, 3.2, 12.8, 12.8, 32);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .623, .669, .144, 1);
.pattern($sphere);
.arc(16, 16, 15, 0, 2 * pi);
.fill;
$sphere.destroy;
}
my $bob_texture = SDL_CreateTexture(
$render, %PIXELFORMAT<ARGB8888>, STATIC, 32, 32
);
SDL_UpdateTexture(
$bob_texture, SDL_Rect.new(:x(0), :y(0), :w(32), :h(32)), $bob.data, $bob.stride // 32
);
SDL_SetTextureBlendMode($bob_texture, 1);
SDL_SetRenderDrawBlendMode($render, 1);
my $event = SDL_Event.new;
my $now = now; # time my $Θ = -π/3; # start angle my $ppi = 500; # scale my $g = -9.81; # accelaration of gravity my $ax = $width/2; # anchor x my $ay = 25; # anchor y my $len = $height - 75; # 'rope' length my $vel; # velocity my $dt; # delta time
main: loop {
while SDL_PollEvent($event) {
my $casted_event = SDL_CastEvent($event);
given $casted_event {
when *.type == QUIT { last main }
when *.type == WINDOWEVENT {
if .event == 5 {
$width = .data1;
$height = .data2;
$ax = $width/2;
$len = $height - 75;
}
}
}
}
$dt = now - $now; $now = now; $vel += $g / $len * sin($Θ) * $ppi * $dt; $Θ += $vel * $dt; my $bx = $ax + sin($Θ) * $len; my $by = $ay + cos($Θ) * $len;
SDL_SetRenderDrawColor($render, 255, 255, 255, 255);
SDL_RenderDrawLine($render, |($ax, $ay, $bx, $by)».round);
SDL_RenderCopy( $render, $bob_texture, Nil,
SDL_Rect.new($bx - 16, $by - 16, 32, 32)
);
SDL_RenderPresent($render);
SDL_SetRenderDrawColor($render, 0, 0, 0, 0);
SDL_RenderClear($render);
}
SDL_Quit();</lang>
REXX
REXX doesn't have a portable graphics user interface (GUI), but
this version is similar to the Ada version and just
displays the coordinates of the end of the pendulum.
<lang rexx>/*REXX program displays the (x, y) coördinates (at the end of a swinging pendulum). */
parse arg cycles Plength theta . /*obtain optional argument from the CL.*/
if cycles== | cycles=="," then cycles= 60 /*Not specified? Then use the default.*/
if pLength== | pLength=="," then pLength= 10 /* " " " " " " */
if theta== | theta=="," then theta= 30 /* " " " " " " */
theta= theta / 180 * pi() /* 'cause that's the way Ada did it. */
was= time('R') /*obtain the current elapsed time (was)*/
g= -9.81 /*gravitation constant (for earth). */
speed= 0 /*velocity of the pendulum, now resting*/
do cycles; call delay 1/20 /*swing the pendulum a number of times.*/
now= time('E') /*obtain the current time (in seconds).*/
duration= now - was /*calculate duration since last cycle. */
acceleration= g / pLength * sin(theta) /*compute the pendulum acceleration. */
x= sin(theta) * pLength /*calculate X coördinate of pendulum.*/
y= cos(theta) * pLength /* " Y " " */
speed= speed + acceleration * duration /*calculate " speed " " */
theta= theta + speed * duration /* " " angle " " */
was= now /*save the elapsed time as it was then.*/
say right('X: ',20) fmt(x) right("Y: ", 10) fmt(y)
end /*cycles*/
exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fmt: procedure; parse arg z; return left(, z>=0)format(z, , digits() - 1) /*align#*/ pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi r2r: return arg(1) // (pi() * 2) /*normalize radians ──► a unit circle. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ cos: procedure; parse arg x; x=r2r(x); numeric fuzz min(6,digits()-3); z=1; _=1; x=x*x
p=z; do k=2 by 2; _=-_*x/(k*(k-1)); z=z+_; if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/ sin: procedure; parse arg x; x=r2r(x); _=x; numeric fuzz min(5, max(1,digits()-3)); q=x*x
z=x; do k=2 by 2 until p=z; p= z; _= -_*q/(k*k+k); z= z+_; end; return z</lang>
Programming note: the SIN and COS functions above are abridged versions.
- output when using the default inputs:
(Shown at three-quarter size.)
X: 5.00000001 Y: 8.66025263
X: 4.99061349 Y: 8.66566514
X: 4.97243576 Y: 8.67610852
X: 4.93067038 Y: 8.69991317
X: 4.89012042 Y: 8.72276910
X: 4.82031857 Y: 8.76153587
X: 4.75801424 Y: 8.79552638
X: 4.68636431 Y: 8.83391049
X: 4.57361919 Y: 8.89280584
X: 4.48234416 Y: 8.93916001
X: 4.37986973 Y: 8.98981271
X: 4.22616556 Y: 9.06308553
X: 4.10234645 Y: 9.11979981
X: 3.92362587 Y: 9.19810621
X: 3.77927439 Y: 9.25835208
X: 3.62636710 Y: 9.31930574
X: 3.41031145 Y: 9.40051989
X: 3.23831928 Y: 9.46114623
X: 3.05856966 Y: 9.52077477
X: 2.80449093 Y: 9.59869639
X: 2.60777314 Y: 9.65399458
X: 2.33706050 Y: 9.72307536
X: 2.12566754 Y: 9.77146685
X: 1.90875333 Y: 9.81614357
X: 1.61409349 Y: 9.86887572
X: 1.38628040 Y: 9.90344528
X: 1.15474731 Y: 9.93310425
X: 0.83894984 Y: 9.96474604
X: 0.60607739 Y: 9.98161664
X: 0.28427382 Y: 9.99595857
X: 0.04337158 Y: 9.99990600
X: -0.19764981 Y: 9.99804656
X: -0.51465016 Y: 9.98674803
X: -0.75351685 Y: 9.97157018
X: -0.99032702 Y: 9.95084184
X: -1.29813435 Y: 9.91538447
X: -1.52787755 Y: 9.88259045
X: -1.82867021 Y: 9.83137708
X: -2.04809904 Y: 9.78801877
X: -2.26218023 Y: 9.74076694
X: -2.53465430 Y: 9.67344838
X: -2.73460510 Y: 9.61883856
X: -2.92771580 Y: 9.56182417
X: -3.17015942 Y: 9.48420212
X: -3.34611403 Y: 9.42356201
X: -3.51412189 Y: 9.36220839
X: -3.72485659 Y: 9.28037935
X: -3.87040178 Y: 9.22062834
X: -4.01043937 Y: 9.16058801
X: -4.18250467 Y: 9.08331710
X: -4.30172468 Y: 9.02746685
X: -4.44332328 Y: 8.95861981
X: -4.54135551 Y: 8.90932543
X: -4.63012036 Y: 8.86351916
X: -4.73113128 Y: 8.81001598
X: -4.79830022 Y: 8.77361372
X: -4.85610202 Y: 8.74175352
X: -4.91679319 Y: 8.70776227
X: -4.95266247 Y: 8.68741106
X: -4.98366742 Y: 8.66966173
Ring
<lang ring>
- Project : Animate a pendulum
load "guilib.ring" load "stdlib.ring"
CounterMan = 1 paint = null pi = 22/7 theta = pi/180*40 g = 9.81 l = 0.50 speed = 0
new qapp
{
win1 = new qwidget() {
setwindowtitle("Animate a pendulum")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
TimerMan = new qtimer(win1)
{
setinterval(1000)
settimeoutevent("draw()")
start()
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
ptime()
endpaint()
}
label1 { setpicture(p1) show() }
return
func ptime()
TimerMan.start()
pPlaySleep()
sleep(0.1)
CounterMan++
if CounterMan = 20
TimerMan.stop()
ok
func pPlaySleep()
pendulum(theta, l)
pendulum(theta, l)
accel = - g * sin(theta) / l / 100
speed = speed + accel / 100
theta = theta + speed
func pendulum(a, l)
pivotx = 640
pivoty = 800
bobx = pivotx + l * 1000 * sin(a)
boby = pivoty - l * 1000 * cos(a)
paint.drawline(pivotx, pivoty, bobx, boby)
paint.drawellipse(bobx + 24 * sin(a), boby - 24 * cos(a), 24, 24)
</lang>
Output video: Animate a pendulum
RLaB
The plane pendulum motion is an interesting and easy problem in which the facilities of RLaB for numerical computation and simulation are easily accessible. The parameters of the problem are , the length of the arm, and the magnitude of the gravity.
We start with the mathematical transliteration of the problem. We solve it in plane (2-D) in terms of describing the angle between the -axis and the arm of the pendulum, where the downwards direction is taken as positive. The Newton equation of motion, which is a second-order non-linear ordinary differential equation (ODE) reads
In our example, we will solve the problem as, so called, initial value problem (IVP). That is, we will specify that at the time t=0 the pendulum was at rest , extended at an angle radians (equivalent to 30 degrees).
RLaB has the facilities to solve ODE IVP which are accessible through odeiv solver. This solver requires that the ODE be written as the first order differential equation,
Here, we introduced a vector , for which the original ODE reads
![{\displaystyle u = [\theta, \dot\theta] = [u_1, u_2]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c775bcc5d8b2d1f0403a15e04d9426763cd3221c)
- .
The RLaB script that solves the problem is
<lang RLaB> // // example: solve ODE for pendulum //
// we first define the first derivative function for the solver dudt = function(t, u, p) {
// t-> time // u->[theta, dtheta/dt ] // p-> g/L, parameter rval = zeros(2,1); rval[1] = u[2]; rval[2] = -p[1] * sin(u[1]); return rval;
};
// now we solve the problem // physical parameters L = 5; // (m), the length of the arm of the pendulum p = mks.g / L; // RLaB has a built-in list 'mks' which contains large number of physical constants and conversion factors T0 = 2*const.pi*sqrt(L/mks.g); // approximate period of the pendulum
// initial conditions theta0 = 30; // degrees, initial angle of deflection of pendulum u0 = [theta0*const.pi/180, 0]; // RLaB has a built-in list 'const' of mathematical constants.
// times at which we want solution t = [0:4:1/64] * T0; // solve for 4 approximate periods with at time points spaced at T0/64
// prepare ODEIV solver optsode = <<>>; optsode.eabs = 1e-6; // relative error for step size optsode.erel = 1e-6; // absolute error for step size optsode.delta_t = 1e-6; // maximum dt that code is allowed optsode.stdout = stderr(); // open the text console and in it print the results of each step of calculation optsode.imethod = 5; // use method No. 5 from the odeiv toolkit, Runge-Kutta 8th order Prince-Dormand method //optsode.phase_space = 0; // the solver returns [t, u1(t), u2(t)] which is default behavior optsode.phase_space = 1; // the solver returns [t, u1(t), u2(t), d(u1)/dt(t), d(u2)/dt]
// solver do my bidding y = odeiv(dudt, p, t, u0, optsode);
// Make an animation. We choose to use 'pgplot' rather then 'gnuplot' interface because the former is // faster and thus less cache-demanding, while the latter can be very cache-demanding (it may slow your // linux system quite down if one sends lots of plots for gnuplot to plot). plwins (1); // we will use one pgplot-window
plwin(1); // plot to pgplot-window No. 1; necessary if using more than one pgplot window plimits (-L,L, -1.25*L, 0.25*L); xlabel ("x-coordinate"); ylabel ("z-coordinate"); plegend ("Arm"); for (i in 1:y.nr) {
// plot a line between the pivot point at (0,0) and the current position of the pendulum arm_line = [0,0; L*sin(y[i;2]), -L*cos(y[i;2])]; // this is because theta is between the arm and the z-coordinate plot (arm_line); sleep (0.1); // sleep 0.1 seconds between plots
}
</lang>
Ruby
This does not have the window resizing handling that Tcl does -- I did not spend enough time in the docs to figure out how to get the new window size out of the configuration event. Of interest when running this pendulum side-by-side with the Tcl one: the Tcl pendulum swings noticibly faster.
<lang ruby>require 'tk'
$root = TkRoot.new("title" => "Pendulum Animation") $canvas = TkCanvas.new($root) do
width 320 height 200 create TkcLine, 0,25,320,25, 'tags' => 'plate', 'width' => 2, 'fill' => 'grey50' create TkcOval, 155,20,165,30, 'tags' => 'pivot', 'outline' => "", 'fill' => 'grey50' create TkcLine, 1,1,1,1, 'tags' => 'rod', 'width' => 3, 'fill' => 'black' create TkcOval, 1,1,2,2, 'tags' => 'bob', 'outline' => 'black', 'fill' => 'yellow'
end $canvas.raise('pivot') $canvas.pack('fill' => 'both', 'expand' => true)
$Theta = 45.0 $dTheta = 0.0 $length = 150 $homeX = 160 $homeY = 25
def show_pendulum
angle = $Theta * Math::PI / 180
x = $homeX + $length * Math.sin(angle)
y = $homeY + $length * Math.cos(angle)
$canvas.coords('rod', $homeX, $homeY, x, y)
$canvas.coords('bob', x-15, y-15, x+15, y+15)
end
def recompute_angle
scaling = 3000.0 / ($length ** 2) # first estimate firstDDTheta = -Math.sin($Theta * Math::PI / 180) * scaling midDTheta = $dTheta + firstDDTheta midTheta = $Theta + ($dTheta + midDTheta)/2 # second estimate midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling midDTheta = $dTheta + (firstDDTheta + midDDTheta)/2 midTheta = $Theta + ($dTheta + midDTheta)/2 # again, first midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling lastDTheta = midDTheta + midDDTheta lastTheta = midTheta + (midDTheta + lastDTheta)/2 # again, second lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2 lastTheta = midTheta + (midDTheta + lastDTheta)/2 # Now put the values back in our globals $dTheta = lastDTheta $Theta = lastTheta
end
def animate
recompute_angle
show_pendulum
$after_id = $root.after(15) {animate}
end
show_pendulum $after_id = $root.after(500) {animate}
$canvas.bind('<Destroy>') {$root.after_cancel($after_id)}
Tk.mainloop</lang>
<lang ruby>Shoes.app(:width => 320, :height => 200) do
@centerX = 160 @centerY = 25 @length = 150 @diameter = 15
@Theta = 45.0 @dTheta = 0.0
stroke gray strokewidth 3 line 0,25,320,25 oval 155,20,10
stroke black @rod = line(@centerX, @centerY, @centerX, @centerY + @length) @bob = oval(@centerX - @diameter, @centerY + @length - @diameter, 2*@diameter)
animate(24) do |i| recompute_angle show_pendulum end
def show_pendulum angle = (90 + @Theta) * Math::PI / 180 x = @centerX + (Math.cos(angle) * @length).to_i y = @centerY + (Math.sin(angle) * @length).to_i
@rod.remove strokewidth 3 @rod = line(@centerX, @centerY, x, y) @bob.move(x-@diameter, y-@diameter) end
def recompute_angle scaling = 3000.0 / (@length **2) # first estimate firstDDTheta = -Math.sin(@Theta * Math::PI / 180) * scaling midDTheta = @dTheta + firstDDTheta midTheta = @Theta + (@dTheta + midDTheta)/2 # second estimate midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling midDTheta = @dTheta + (firstDDTheta + midDDTheta)/2 midTheta = @Theta + (@dTheta + midDTheta)/2 # again, first midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling lastDTheta = midDTheta + midDDTheta lastTheta = midTheta + (midDTheta + lastDTheta)/2 # again, second lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2 lastTheta = midTheta + (midDTheta + lastDTheta)/2 # Now put the values back in our globals @dTheta = lastDTheta @Theta = lastTheta end
end</lang>
<lang ruby>#!/bin/ruby
begin; require 'rubygems'; rescue; end
require 'gosu' include Gosu
- Screen size
W = 640 H = 480
- Full-screen mode
FS = false
- Screen update rate (Hz)
FPS = 60
class Pendulum
attr_accessor :theta, :friction
def initialize( win, x, y, length, radius, bob = true, friction = false) @win = win @centerX = x @centerY = y @length = length @radius = radius @bob = bob @friction = friction
@theta = 60.0 @omega = 0.0 @scale = 2.0 / FPS end
def draw
@win.translate(@centerX, @centerY) {
@win.rotate(@theta) {
@win.draw_quad(-1, 0, 0x3F_FF_FF_FF, 1, 0, 0x3F_FF_FF_00, 1, @length, 0x3F_FF_FF_00, -1, @length, 0x3F_FF_FF_FF )
if @bob
@win.translate(0, @length) {
@win.draw_quad(0, -@radius, Color::RED, @radius, 0, Color::BLUE, 0, @radius, Color::WHITE, -@radius, 0, Color::BLUE )
}
end
}
}
end
def update # Thanks to Hugo Elias for the formula (and explanation thereof) @theta += @omega @omega = @omega - (Math.sin(@theta * Math::PI / 180) / (@length * @scale)) @theta *= 0.999 if @friction end
end # Pendulum class
class GfxWindow < Window
def initialize # Initialize the base class super W, H, FS, 1.0 / FPS * 1000 # self.caption = "You're getting sleeeeepy..." self.caption = "Ruby/Gosu Pendulum Simulator (Space toggles friction)"
@n = 1 # Try changing this number!
@pendulums = []
(1..@n).each do |i|
@pendulums.push Pendulum.new( self, W / 2, H / 10, H * 0.75 * (i / @n.to_f), H / 60 )
end
end
def draw
@pendulums.each { |pen| pen.draw }
end
def update
@pendulums.each { |pen| pen.update }
end
def button_up(id)
if id == KbSpace
@pendulums.each { |pen|
pen.friction = !pen.friction
pen.theta = (pen.theta <=> 0) * 45.0 unless pen.friction
}
else
close
end
end
def needs_cursor?() true end
end # GfxWindow class
begin
GfxWindow.new.show
rescue Exception => e
puts e.message, e.backtrace gets
end</lang>
Rust
This is a translation of the C# code, albeit with a more explicit declaration of constants.
When moving the mouse over the viewport, the framerate accelerates somehow - any edits to keep the framerate constant is welcome!
<lang Rust> // using version 0.107.0 of piston_window use piston_window::{clear, ellipse, line_from_to, PistonWindow, WindowSettings};
const PI: f64 = std::f64::consts::PI; const WIDTH: u32 = 640; const HEIGHT: u32 = 480;
const ANCHOR_X: f64 = WIDTH as f64 / 2. - 12.; const ANCHOR_Y: f64 = HEIGHT as f64 / 4.; const ANCHOR_ELLIPSE: [f64; 4] = [ANCHOR_X - 3., ANCHOR_Y - 3., 6., 6.];
const ROPE_ORIGIN: [f64; 2] = [ANCHOR_X, ANCHOR_Y]; const ROPE_LENGTH: f64 = 200.; const ROPE_THICKNESS: f64 = 1.;
const DELTA: f64 = 0.05; const STANDARD_GRAVITY_VALUE: f64 = -9.81;
// RGBA Colors const BLACK: [f32; 4] = [0., 0., 0., 1.]; const RED: [f32; 4] = [1., 0., 0., 1.]; const GOLD: [f32; 4] = [216. / 255., 204. / 255., 36. / 255., 1.0]; fn main() {
let mut window: PistonWindow = WindowSettings::new("Pendulum", [WIDTH, HEIGHT])
.exit_on_esc(true)
.build()
.unwrap();
let mut angle = PI / 2.; let mut angular_vel = 0.;
while let Some(event) = window.next() {
let (angle_sin, angle_cos) = angle.sin_cos();
let ball_x = ANCHOR_X + angle_sin * ROPE_LENGTH;
let ball_y = ANCHOR_Y + angle_cos * ROPE_LENGTH;
let angle_accel = STANDARD_GRAVITY_VALUE / ROPE_LENGTH * angle_sin;
angular_vel += angle_accel * DELTA;
angle += angular_vel * DELTA;
let rope_end = [ball_x, ball_y];
let ball_ellipse = [ball_x - 7., ball_y - 7., 14., 14.];
window.draw_2d(&event, |context, graphics, _device| {
clear([1.0; 4], graphics);
line_from_to(
BLACK,
ROPE_THICKNESS,
ROPE_ORIGIN,
rope_end,
context.transform,
graphics,
);
ellipse(RED, ANCHOR_ELLIPSE, context.transform, graphics);
ellipse(GOLD, ball_ellipse, context.transform, graphics);
});
}
} </lang>
Scala
<lang Scala>import java.awt.Color import java.util.concurrent.{Executors, TimeUnit}
import scala.swing.{Graphics2D, MainFrame, Panel, SimpleSwingApplication} import scala.swing.Swing.pair2Dimension
object Pendulum extends SimpleSwingApplication {
val length = 100
lazy val ui = new Panel {
import scala.math.{cos, Pi, sin}
background = Color.white preferredSize = (2 * length + 50, length / 2 * 3) peer.setDoubleBuffered(true)
var angle: Double = Pi / 2
override def paintComponent(g: Graphics2D): Unit = {
super.paintComponent(g)
val (anchorX, anchorY) = (size.width / 2, size.height / 4)
val (ballX, ballY) =
(anchorX + (sin(angle) * length).toInt, anchorY + (cos(angle) * length).toInt)
g.setColor(Color.lightGray)
g.drawLine(anchorX - 2 * length, anchorY, anchorX + 2 * length, anchorY)
g.setColor(Color.black)
g.drawLine(anchorX, anchorY, ballX, ballY)
g.fillOval(anchorX - 3, anchorY - 4, 7, 7)
g.drawOval(ballX - 7, ballY - 7, 14, 14)
g.setColor(Color.yellow)
g.fillOval(ballX - 7, ballY - 7, 14, 14)
}
val animate: Runnable = new Runnable {
var angleVelocity = 0.0
var dt = 0.1
override def run(): Unit = {
angleVelocity += -9.81 / length * Math.sin(angle) * dt
angle += angleVelocity * dt
repaint()
}
}
}
override def top = new MainFrame {
title = "Rosetta Code >>> Task: Animate a pendulum | Language: Scala"
contents = ui
centerOnScreen()
Executors.
newSingleThreadScheduledExecutor().
scheduleAtFixedRate(ui.animate, 0, 15, TimeUnit.MILLISECONDS)
}
}</lang>
Scheme
This is a direct translation of the Ruby/Tk example into Scheme + PS/Tk.
<lang scheme>#!r6rs
- R6RS implementation of Pendulum Animation
(import (rnrs)
(lib pstk main) ; change this for your pstk installation
)
(define PI 3.14159) (define *conv-radians* (/ PI 180)) (define *theta* 45.0) (define *d-theta* 0.0) (define *length* 150) (define *home-x* 160) (define *home-y* 25)
- estimates new angle of pendulum
(define (recompute-angle)
(define (avg a b) (/ (+ a b) 2))
(let* ((scaling (/ 3000.0 (* *length* *length*)))
; first estimate
(first-dd-theta (- (* (sin (* *theta* *conv-radians*)) scaling)))
(mid-d-theta (+ *d-theta* first-dd-theta))
(mid-theta (+ *theta* (avg *d-theta* mid-d-theta)))
; second estimate
(mid-dd-theta (- (* (sin (* mid-theta *conv-radians*)) scaling)))
(mid-d-theta-2 (+ *d-theta* (avg first-dd-theta mid-dd-theta)))
(mid-theta-2 (+ *theta* (avg *d-theta* mid-d-theta-2)))
; again first
(mid-dd-theta-2 (- (* (sin (* mid-theta-2 *conv-radians*)) scaling)))
(last-d-theta (+ mid-d-theta-2 mid-dd-theta-2))
(last-theta (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta)))
; again second
(last-dd-theta (- (* (sin (* last-theta *conv-radians*)) scaling)))
(last-d-theta-2 (+ mid-d-theta-2 (avg mid-dd-theta-2 last-dd-theta)))
(last-theta-2 (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta-2))))
; put values back in globals
(set! *d-theta* last-d-theta-2)
(set! *theta* last-theta-2)))
- The main event loop and graphics context
(let ((tk (tk-start)))
(tk/wm 'title tk "Pendulum Animation") (let ((canvas (tk 'create-widget 'canvas)))
;;; redraw the pendulum on canvas
;;; - uses angle and length to compute new (x,y) position of bob
(define (show-pendulum canvas)
(let* ((pendulum-angle (* *conv-radians* *theta*))
(x (+ *home-x* (* *length* (sin pendulum-angle))))
(y (+ *home-y* (* *length* (cos pendulum-angle)))))
(canvas 'coords 'rod *home-x* *home-y* x y)
(canvas 'coords 'bob (- x 15) (- y 15) (+ x 15) (+ y 15))))
;;; move the pendulum and repeat after 20ms
(define (animate)
(recompute-angle)
(show-pendulum canvas)
(tk/after 20 animate))
;; layout the canvas (tk/grid canvas 'column: 0 'row: 0) (canvas 'create 'line 0 25 320 25 'tags: 'plate 'width: 2 'fill: 'grey50) (canvas 'create 'oval 155 20 165 30 'tags: 'pivot 'outline: "" 'fill: 'grey50) (canvas 'create 'line 1 1 1 1 'tags: 'rod 'width: 3 'fill: 'black) (canvas 'create 'oval 1 1 2 2 'tags: 'bob 'outline: 'black 'fill: 'yellow)
;; get everything started (show-pendulum canvas) (tk/after 500 animate) (tk-event-loop tk)))
</lang>
Scilab
The animation is displayed on a graphic window, and won't stop until it shows all positions calculated unless the user abort the execution on Scilab console. <lang>//Input variables (Assumptions: massless pivot, no energy loss) bob_mass=10; g=-9.81; L=2; theta0=-%pi/6; v0=0; t0=0;
//No. of steps steps=300;
//Setting deltaT or duration (comment either of the lines below) //deltaT=0.1; t_max=t0+deltaT*steps; t_max=5; deltaT=(t_max-t0)/steps;
if t_max<=t0 then
error("Check duration (t0 and t_f), number of steps and deltaT.");
end
//Initial position not_a_pendulum=%F; t=zeros(1,steps); t(1)=t0; //time theta=zeros(1,steps); theta(1)=theta0; //angle F=zeros(1,steps); F(1)=bob_mass*g*sin(theta0); //force A=zeros(1,steps); A(1)=F(1)/bob_mass; //acceleration V=zeros(1,steps); V(1)=v0; //linear speed W=zeros(1,steps); W(1)=v0/L; //angular speed
for i=2:steps
t(i)=t(i-1)+deltaT;
V(i)=A(i-1)*deltaT+V(i-1);
W(i)=V(i)/L;
theta(i)=theta(i-1)+W(i)*deltaT;
F(i)=bob_mass*g*sin(theta(i));
A(i)=F(i)/bob_mass;
if (abs(theta(i))>=%pi | (abs(theta(i))==0 & V(i)==0)) & ~not_a_pendulum then
disp("Initial conditions do not describe a pendulum.");
not_a_pendulum = %T;
end
end clear i
//Ploting the pendulum bob_r=0.08*L; bob_shape=bob_r*exp(%i.*linspace(0,360,20)/180*%pi);
bob_pos=zeros(20,steps); rod_pos=zeros(1,steps); for i=1:steps
rod_pos(i)=L*exp(%i*(-%pi/2+theta(i))); bob_pos(:,i)=bob_shape'+rod_pos(i);
end clear i
scf(0); clf(); xname("Simple gravity pendulum"); plot2d(real([0 rod_pos(1)]),imag([0 rod_pos(1)])); axes=gca(); axes.isoview="on"; axes.children(1).children.mark_style=3; axes.children(1).children.mark_size=1; axes.children(1).children.thickness=3;
plot2d(real(bob_pos(:,1)),imag(bob_pos(:,1))); axes=gca(); axes.children(1).children.fill_mode="on"; axes.children(1).children.foreground=2; axes.children(1).children.background=2;
if max(imag(bob_pos))>0 then
axes.data_bounds=[-L-bob_r,-L-1.01*bob_r;L+bob_r,max(imag(bob_pos))];
else
axes.data_bounds=[-L-bob_r,-L-1.01*bob_r;L+bob_r,bob_r];
end
//Animating the plot disp("Duration: "+string(max(t)+deltaT-t0)+"s."); sleep(850); for i=2:steps
axes.children(1).children.data=[real(bob_pos(:,i)), imag(bob_pos(:,i))]; axes.children(2).children.data=[0, 0; real(rod_pos(i)), imag(rod_pos(i))]; sleep(deltaT*1000)
end clear i</lang>
SequenceL
Using the Easel Engine for SequenceL
<lang sequencel>import <Utilities/Sequence.sl>;
import <Utilities/Conversion.sl>;
import <Utilities/Math.sl>;
//region Types
Point ::= (x: int(0), y: int(0)); Color ::= (red: int(0), green: int(0), blue: int(0)); Image ::= (kind: char(1), iColor: Color(0), vert1: Point(0), vert2: Point(0), vert3: Point(0), center: Point(0),
radius: int(0), height: int(0), width: int(0), message: char(1), source: char(1));
Click ::= (clicked: bool(0), clPoint: Point(0)); Input ::= (iClick: Click(0), keys: char(1));
//endregion
//region Helpers======================================================================
//region Constructor-Functions-------------------------------------------------
point(a(0), b(0)) := (x: a, y: b);
color(r(0), g(0), b(0)) := (red: r, green: g, blue: b);
segment(e1(0), e2(0), c(0)) := (kind: "segment", vert1: e1, vert2: e2, iColor: c);
disc(ce(0), rad(0), c(0)) := (kind: "disc", center: ce, radius: rad, iColor: c);
//endregion----------------------------------------------------------------------
//region Colors---------------------------------------------------------------- dBlack := color(0, 0, 0); dYellow := color(255, 255, 0); //endregion---------------------------------------------------------------------- //endregion=============================================================================
//=================Easel=Functions=============================================
State ::= (angle: float(0), angleVelocity: float(0), angleAccel: float(0));
initialState := (angle: pi/2, angleVelocity: 0.0, angleAccel: 0.0);
dt := 0.3; length := 450;
anchor := point(500, 750);
newState(I(0), S(0)) :=
let
newAngle := S.angle + newAngleVelocity * dt;
newAngleVelocity := S.angleVelocity + newAngleAccel * dt;
newAngleAccel := -9.81 / length * sin(S.angle);
in
(angle: newAngle, angleVelocity: newAngleVelocity, angleAccel: newAngleAccel);
sounds(I(0), S(0)) := ["ding"] when I.iClick.clicked else [];
images(S(0)) :=
let
pendulum := pendulumLocation(S.angle);
in
[segment(anchor, pendulum, dBlack),
disc(pendulum, 30, dYellow),
disc(anchor, 5, dBlack)];
pendulumLocation(angle) :=
let
x := anchor.x + round(sin(angle) * length);
y := anchor.y - round(cos(angle) * length);
in
point(x, y);
//=============End=Easel=Functions=============================================</lang>
- Output:
Sidef
<lang ruby>require('Tk')
var root = %s<MainWindow>.new('-title' => 'Pendulum Animation') var canvas = root.Canvas('-width' => 320, '-height' => 200)
canvas.createLine( 0, 25, 320, 25, '-tags' => <plate>, '-width' => 2, '-fill' => :grey50) canvas.createOval(155, 20, 165, 30, '-tags' => <pivot outline>, '-fill' => :grey50) canvas.createLine( 1, 1, 1, 1, '-tags' => <rod width>, '-width' => 3, '-fill' => :black) canvas.createOval( 1, 1, 2, 2, '-tags' => <bob outline>, '-fill' => :yellow)
canvas.raise(:pivot) canvas.pack('-fill' => :both, '-expand' => 1) var(θ = 45, Δθ = 0, length = 150, homeX = 160, homeY = 25)
func show_pendulum() {
var angle = θ.deg2rad var x = (homeX + length*sin(angle)) var y = (homeY + length*cos(angle)) canvas.coords(:rod, homeX, homeY, x, y) canvas.coords(:bob, x - 15, y - 15, x + 15, y + 15)
}
func recompute_angle() {
var scaling = 3000/(length**2)
# first estimate var firstΔΔθ = (-sin(θ.deg2rad) * scaling) var midΔθ = (Δθ + firstΔΔθ) var midθ = ((Δθ + midΔθ)/2 + θ)
# second estimate var midΔΔθ = (-sin(midθ.deg2rad) * scaling) midΔθ = ((firstΔΔθ + midΔΔθ)/2 + Δθ) midθ = ((Δθ + midΔθ)/2 + θ)
# again, first midΔΔθ = (-sin(midθ.deg2rad) * scaling) var lastΔθ = (midΔθ + midΔΔθ) var lastθ = ((midΔθ + lastΔθ)/2 + midθ)
# again, second var lastΔΔθ = (-sin(lastθ.deg2rad) * scaling) lastΔθ = ((midΔΔθ + lastΔΔθ)/2 + midΔθ) lastθ = ((midΔθ + lastΔθ)/2 + midθ)
# Now put the values back in our globals Δθ = lastΔθ θ = lastθ
}
func animate(Ref id) {
recompute_angle()
show_pendulum()
*id = root.after(15 => { animate(id) })
}
show_pendulum() var after_id = root.after(500 => { animate(\after_id) })
canvas.bind('<Destroy>' => { after_id.cancel }) %S<Tk>.MainLoop()</lang>
smart BASIC
<lang smart BASIC>'Pendulum 'By Dutchman ' --- constants g=9.81 ' accelleration of gravity l=1 ' length of pendulum GET SCREEN SIZE sw,sh pivotx=sw/2 pivoty=150 ' --- initialise graphics GRAPHICS DRAW COLOR 1,0,0 FILL COLOR 0,0,1 DRAW SIZE 2 ' --- initialise pendulum theta=1 ' initial displacement in radians speed=0 ' --- loop DO
bobx=pivotx+100*l*SIN(theta) boby=pivoty-100*l*COS(theta) GOSUB Plot PAUSE 0.01 accel=g*SIN(theta)/l/100 speed=speed+accel theta=theta+speed
UNTIL 0 END ' --- subroutine Plot: REFRESH OFF GRAPHICS CLEAR 1,1,0.5 DRAW LINE pivotx,pivoty TO bobx,boby FILL CIRCLE bobx,boby SIZE 10 REFRESH ON RETURN </lang>
We hope that the webmaster will soon have image uploads enabled again so that we can show a screen shot.
Tcl
<lang tcl>package require Tcl 8.5 package require Tk
- Make the graphical entities
pack [canvas .c -width 320 -height 200] -fill both -expand 1 .c create line 0 25 320 25 -width 2 -fill grey50 -tags plate .c create line 1 1 1 1 -tags rod -width 3 -fill black .c create oval 1 1 2 2 -tags bob -fill yellow -outline black .c create oval 155 20 165 30 -fill grey50 -outline {} -tags pivot
- Set some vars
set points {} set Theta 45.0 set dTheta 0.0 set pi 3.1415926535897933 set length 150 set homeX 160
- How to respond to a changing in size of the window
proc resized {width} {
global homeX
.c coords plate 0 25 $width 25
set homeX [expr {$width / 2}]
.c coords pivot [expr {$homeX-5}] 20 [expr {$homeX+5}] 30
showPendulum
}
- How to actually arrange the pendulum, mapping the model to the display
proc showPendulum {} {
global Theta dTheta pi length homeX
set angle [expr {$Theta * $pi/180}]
set x [expr {$homeX + $length*sin($angle)}]
set y [expr {25 + $length*cos($angle)}]
.c coords rod $homeX 25 $x $y
.c coords bob [expr {$x-15}] [expr {$y-15}] [expr {$x+15}] [expr {$y+15}]
}
- The dynamic part of the display
proc recomputeAngle {} {
global Theta dTheta pi length
set scaling [expr {3000.0/$length**2}]
# first estimate
set firstDDTheta [expr {-sin($Theta * $pi/180)*$scaling}]
set midDTheta [expr {$dTheta + $firstDDTheta}]
set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
# second estimate
set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
set midDTheta [expr {$dTheta + ($firstDDTheta + $midDDTheta)/2}]
set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
# Now we do a double-estimate approach for getting the final value
# first estimate
set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
set lastDTheta [expr {$midDTheta + $midDDTheta}]
set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
# second estimate
set lastDDTheta [expr {-sin($lastTheta * $pi/180)*$scaling}]
set lastDTheta [expr {$midDTheta + ($midDDTheta + $lastDDTheta)/2}]
set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
# Now put the values back in our globals
set dTheta $lastDTheta
set Theta $lastTheta
}
- Run the animation by updating the physical model then the display
proc animate {} {
global animation
recomputeAngle showPendulum
# Reschedule set animation [after 15 animate]
} set animation [after 500 animate]; # Extra initial delay is visually pleasing
- Callback to handle resizing of the canvas
bind .c <Configure> {resized %w}
- Callback to stop the animation cleanly when the GUI goes away
bind .c <Destroy> {after cancel $animation}</lang>
Wren
<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window import "math" for Math import "./dynamic" for Tuple
var Element = Tuple.create("Element", ["x", "y"]) var Dt = 0.1 var Angle = Num.pi / 2 var AngleVelocity = 0
class Pendulum {
construct new(length) {
Window.title = "Pendulum"
_w = 2 * length + 50
_h = length / 2 * 3
Window.resize(_w, _h)
Canvas.resize(_w, _h)
_length = length
_anchor = Element.new((_w/2).floor, (_h/4).floor)
_fore = Color.black
}
init() {
drawPendulum()
}
drawPendulum() {
Canvas.cls(Color.white)
var ball = Element.new((_anchor.x + Math.sin(Angle) * _length).truncate,
(_anchor.y + Math.cos(Angle) * _length).truncate)
Canvas.line(_anchor.x, _anchor.y, ball.x, ball.y, _fore, 2)
Canvas.circlefill(_anchor.x - 3, _anchor.y - 4, 7, Color.lightgray)
Canvas.circle(_anchor.x - 3, _anchor.y - 4, 7, _fore)
Canvas.circlefill(ball.x - 7, ball.y - 7, 14, Color.yellow)
Canvas.circle(ball.x - 7, ball.y - 7, 14, _fore)
}
update() {
AngleVelocity = AngleVelocity - 9.81 / _length * Math.sin(Angle) * Dt
Angle = Angle + AngleVelocity * Dt
}
draw(alpha) {
drawPendulum()
}
}
var Game = Pendulum.new(200)</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations
proc Ball(X0, Y0, R, C); \Draw a filled circle int X0, Y0, R, C; \center coordinates, radius, color int X, Y; for Y:= -R to R do
for X:= -R to R do
if X*X + Y*Y <= R*R then Point(X+X0, Y+Y0, C);
def L = 2.0, \pendulum arm length (meters)
G = 9.81, \acceleration due to gravity (meters/second^2)
Pi = 3.14,
DT = 1.0/72.0; \delta time = screen refresh rate (seconds)
def X0=640/2, Y0=480/2; \anchor point = center coordinate real S, V, A, T; \arc length, velocity, acceleration, theta angle int X, Y; \ball coordinates
[SetVid($101); \set 640x480x8 graphic display mode T:= Pi*0.75; V:= 0.0; \starting angle and velocity S:= T*L; repeat A:= -G*Sin(T);
V:= V + A*DT;
S:= S + V*DT;
T:= S/L;
X:= X0 + fix(L*100.0*Sin(T)); \100 scales to fit screen
Y:= Y0 + fix(L*100.0*Cos(T));
Move(X0, Y0); Line(X, Y, 7); \draw pendulum
Ball(X, Y, 10, $E\yellow\);
while port($3DA) & $08 do []; \wait for vertical retrace to go away
repeat until port($3DA) & $08; \wait for vertical retrace signal
Move(X0, Y0); Line(X, Y, 0); \erase pendulum
Ball(X, Y, 10, 0\black\);
until KeyHit; \keystroke terminates program SetVid(3); \restore normal text screen ]</lang>
Yabasic
<lang Yabasic>clear screen open window 400, 300 window origin "cc"
rodLen = 160 gravity = 2 damp = .989 TWO_PI = pi * 2 angle = 90 * 0.01745329251 // convert degree to radian
repeat
acceleration = -gravity / rodLen * sin(angle) angle = angle + velocity : if angle > TWO_PI angle = 0 velocity = velocity + acceleration velocity = velocity * damp posX = sin(angle) * rodLen posY = cos(angle) * rodLen - 70 clear window text -50, -100, "Press 'q' to quit" color 250, 0, 250 fill circle 0, -70, 4 line 0, -70, posX, posY color 250, 100, 20 fill circle posX, posY, 10
until(lower$(inkey$(0.02)) = "q")
exit</lang>
ZX Spectrum Basic
In a real Spectrum it is too slow. Use the BasinC emulator/editor at maximum speed for realistic animation. <lang zxbasic>10 OVER 1: CLS 20 LET theta=1 30 LET g=9.81 40 LET l=0.5 50 LET speed=0 100 LET pivotx=120 110 LET pivoty=140 120 LET bobx=pivotx+l*100*SIN (theta) 130 LET boby=pivoty+l*100*COS (theta) 140 GO SUB 1000: PAUSE 1: GO SUB 1000 190 LET accel=g*SIN (theta)/l/100 200 LET speed=speed+accel/100 210 LET theta=theta+speed 220 GO TO 100 1000 PLOT pivotx,pivoty: DRAW bobx-pivotx,boby-pivoty 1010 CIRCLE bobx,boby,3 1020 RETURN</lang>
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