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.
For this 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++
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.
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>
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>
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>
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.
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>
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); >
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:
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>
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.
| -------------------------------------------------|-------------------------------------------------- | | | | | | | | | | | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | | | | | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | | | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | | | | | | | | | | -------------------------------------------------|-------------------------------------------------- | | | | G | #G# | #GOG# | #G# | G | | | | | | | | | | | | | | | | | | | | | |
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 0.01lastPaintedAt <- 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>
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>
With <SVG>
With some control elements to ease the usage. <lang javascript><html> <head> <title>Swinging Pendulum Simulation</title> </head>
<body>
<svg id="scene" height="200" width="300">
<line id="string" x1="150" y1="50" x2="250" y2="50" stroke="brown" stroke-width="4" />
<circle id="ball" cx="250" cy="50" r="20" fill="black" />
</svg>
Initial angle:<input id="in_angle" type="number" min="0" max="180" onchange="condReset()"/>(degrees)
<button type="button" onclick="startAnimation()">Start</button>
<button type="button" onclick="stopAnimation()">Stop</button>
<button type="button" onclick="reset()">Reset</button>
<script>
in_angle.value = 0;
var cx = 150, cy = 50;
var radius = 100; // cm
var g = 9.81; // m/s^2
var angle = 0; // radians
var vel = 0; // m/s
var dx = 0.02; // s
var acc, vel, penx, peny;
var timerFunction = null;
function stopAnimation() {
if(timerFunction != null){
clearInterval(timerFunction);
timerFunction = null;
}
}
function startAnimation() {
if(!timerFunction) timerFunction = setInterval(swing, dx * 1000);
}
function swing(){
acc = g * Math.cos(angle);
vel += acc * dx;//Convert m/s/s to m/s
angle += vel/(radius/100) * dx; //convert m/s into rad/s and then into rad
setPenPos();
}
function setPenPos(){
penx = cx + radius * Math.cos(angle);
peny = cy + radius * Math.sin(angle);
scene.getElementById("string").setAttribute("x2", penx);
scene.getElementById("string").setAttribute("y2", peny);
scene.getElementById("ball").setAttribute("cx", penx);
scene.getElementById("ball").setAttribute("cy", peny);
}
function reset(){
var val = parseInt(in_angle.value)*0.0174532925199;
if (val) angle = val;
else angle = 0;
acc = 0;
vel = 0;
setPenPos();
}
function condReset(){
if (!timerFunction) reset();
}
</script>
</body>
</html></lang>
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 = linspace(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(t,u,du) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ)) bc2(residual, ua, ub) = (residual[1] = ua[1] + pi/2; residual[2] = ub[1] + pi/2) bvp2 = TwoPointBVProblem(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>
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>
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 - Perl 6', 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>
Phix
<lang Phix>-- demo\rosetta\animate_pendulum2.exw include pGUI.e
Ihandle dlg, canvas, timer cdCanvas cdcanvas
constant g = 50
atom angle = PI/2,
velocity = 0
integer w, h, len = 0
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
{w, h} = IupGetIntInt(canvas, "DRAWSIZE") cdCanvasActivate(cdcanvas) cdCanvasClear(cdcanvas) -- new suspension point: integer sX = floor(w/2) integer sY = floor(h/16) -- 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*/)
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 delta = -len*sin(angle)*g velocity += dt*delta angle += dt*velocity IupUpdate(canvas) return IUP_IGNORE
end function
function map_cb(Ihandle ih)
atom res = IupGetDouble(NULL, "SCREENDPI")/25.4 IupGLMakeCurrent(canvas) cdcanvas = cdCreateCanvas(CD_GL, "10x10 %g", {res}) 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
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupGLCanvas() IupSetAttribute(canvas, "RASTERSIZE", "640x380") 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") IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) IupMainLoop() IupClose()
end procedure
main()</lang>
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>
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>
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
- .
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>
Scala
<lang Scala>import java.awt.Color import scala.actors.Actor 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
def pendular = new Actor { var angleVelocity = 0.0 val dt = 0.1
def act() { while (true) { angleVelocity += (-9.81 / length * sin(angle)) * dt angle += angleVelocity * dt repaint() Thread.sleep(15) } } }
override def paintComponent(g: Graphics2D) = { 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) } }
def top = new MainFrame { title = "Rosetta Code >>> Task: Animate a pendulum | Language: Scala" contents = ui centerOnScreen ui.pendular.start }
}</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>
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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