Orbital elements: Difference between revisions
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<pre>Position : (0.787295801413, 0.454545489549, 0.0)
Speed : (-0.547722599684, 0.948683273698, 0.0)</pre>
={{header|REXX}}==
{{trans|Java}}
Vectors are represented by strings: 'x/y/z'
<lang rexx>/* REXX */
Numeric Digits 16
Parse Value orbitalStateVectors(1.0,0.1,0.0,355.0/(113.0*6.0),0.0,0.0),
With position speed
Say "Position :" tostring(position)
Say "Speed :" tostring(speed)
Exit
orbitalStateVectors: Procedure
Parse Arg semimajorAxis,,
eccentricity,,
inclination,,
longitudeOfAscendingNode,,
argumentOfPeriapsis,,
trueAnomaly
i='1/0/0'
j='0/1/0'
k='0/0/1'
Parse Value rotate(i, j, longitudeOfAscendingNode) With i j
Parse Value rotate(j, k, inclination) With j p
Parse Value rotate(i, j, argumentOfPeriapsis) With i j
If eccentricity=1 Then l=2
Else l=1-eccentricity*eccentricity
l=l*semimajorAxis
c=my_cos(trueAnomaly)
s=my_sin(trueAnomaly)
r=l/(1+eccentricity*c)
rprime=s*r*r/l
position=vmultiply(mulAdd(i,c,j,s),r)
speed=mulAdd(i,rprime*c-r*s,j,rprime*s+r*c)
speed=vdivide(speed,abs(speed))
speed=vmultiply(speed,my_sqrt(2.0/r-1.0/semimajorAxis))
Return position speed
abs: Procedure
Parse Arg v.x '/' v.y '/' v.z
Return my_sqrt(v.x**2+v.y**2+v.z**2)
muladd: Procedure
Parse Arg v1,x1,v2,x2
Parse Var v1 v1.x '/' v1.y '/' v1.z
Parse Var v2 v2.x '/' v2.y '/' v2.z
z=(v1.x*x1+v2.x*x2)||'/'||(v1.y*x1+v2.y*x2)||'/'||(v1.z*x1+v2.z*x2)
Return z
rotate: Procedure
Parse Arg i,j,alpha
xx=mulAdd(i,my_cos(alpha,16,'R'),j,my_sin(alpha,16,'R'))
yy=mulAdd(i,-my_sin(alpha,16,'R'),j,my_cos(alpha,16,'R'))
Return xx yy
vmultiply: Procedure
Parse Arg v,d
Parse Var v v.x '/' v.y '/' v.z
Return (v.x*d)||'/'||(v.y*d)||'/'||(v.z*d)
vdivide: Procedure
Parse Arg v,d
Parse Var v v.x '/' v.y '/' v.z
Return (v.x/d)||'/'||(v.y/d)||'/'||(v.z/d)
tostring:
Parse Arg v.x '/' v.y '/' v.z
Return '('v.x','v.y','v.z')'
my_sqrt: Procedure
/* REXX ***************************************************************
* EXEC to calculate the square root of a = 2 with high precision
**********************************************************************/
Parse Arg x,prec
If prec<9 Then prec=9
prec1=2*prec
eps=10**(-prec1)
k = 1
Numeric Digits 3
r0= x
r = 1
Do i=1 By 1 Until r=r0 | ('ABS'(r*r-x)<eps)
r0 = r
r = (r + x/r) / 2
k = min(prec1,2*k)
Numeric Digits (k + 5)
End
Numeric Digits prec
Return r+0
my_sin: Procedure
/* REXX ****************************************************************
* Return my_sin(x<,p>) -- with the specified precision
* my_sin(x) = x-(x**3/3!)+(x**5/5!)-(x**7/7!)+-...
***********************************************************************/
Parse Arg x,prec
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz 3
pi=pi(2*prec)
Do While x>pi
x=x-pi
End
Do While x<-pi
x=x+pi
End
o=x
u=1
r=x
Do i=3 By 2
ra=r
o=-o*x*x
u=u*i*(i-1)
r=r+(o/u)
If r=ra Then Leave
End
Numeric Digits prec
Return r+0
my_cos: Procedure
/* REXX ****************************************************************
* Return my_cos(x) -- with specified precision
* my_cos(x) = 1-(x**2/2!)+(x**4/4!)-(x**6/6!)+-...
***********************************************************************/
Parse Arg x,prec
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz 3
o=1
u=1
r=1
Do i=1 By 2
ra=r
o=-o*x*x
u=u*i*(i+1)
r=r+(o/u)
If r=ra Then Leave
End
Numeric Digits prec
Return r+0</lang>
{{out}}
<pre>Position : (0.7794228433986798,0.4500000346536842,0)
Speed : (-0.5527708425678772,0.9574270859639177,0)</pre>
=={{header|Scala}}==
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