I'm attempting to make an animation that models the 3-body problem, with not
much success. I no matter what I set the starting parameters to, nothing
ever goes into orbit, which leads me to believe that my physics are screwed
up.

The source is:
#include "colors.inc"
#include "math.inc"

#declare massA = .5;
#declare massB = .5;
#declare massC = .5;

global_settings {max_trace_level 5}

camera {location <10,-20,10> look_at <-10,20,-10> sky <0, 0, 1>}


light_source {<-140,-200,300> rgb <1.0, 1.0, 0.95>*1.5}
light_source {<140,-200,-300> rgb <0.9, 0.9, 1.00>*0.8 shadowless}

//axes
cylinder {<0, 0, 0>, <2, 0, 0>, .1 pigment {color Red}}
cylinder {<0, 0, 0>, <0, 2, 0>, .1 pigment {color Green}}
cylinder {<0, 0, 0>, <0, 0, 2>, .1 pigment {color Blue}}

#include "orbitdata.inc"

sphere {<px1, py1, pz1>, .5 pigment{color Cyan}}

sphere {<px2, py2, pz2>, .5 pigment{color Magenta}}

sphere {<px3, py3, pz3>, .5 pigment{color Yellow}}

#fopen nextpos "orbitdata.inc" write

/////////////////////////////////////////////////////////////////////ball A
#write (nextpos, "#declare px1= ", str((px1+vx1), 0, -1), ";n")
#write (nextpos, "#declare py1= ", str((py1+vy1), 0, -1), ";n")
#write (nextpos, "#declare pz1= ", str((pz1+vz1), 0, -1), ";nn")

#declare distSB = (px1-px2)*(px1-px2) + (py1-py2)*(py1-py2) +
(pz1-pz2)*(pz1-pz2);
#declare distSC = (px1-px3)*(px1-px3) + (py1-py3)*(py1-py3) +
(pz1-pz3)*(pz1-pz3);

#declare ax = -((massA*massB)/distSB)*sgn(px1-px2) -
((massA*massC)/distSC)*sgn(px1-px3);
#declare ay = -((massA*massB)/distSB)*sgn(py1-py2) -
((massA*massC)/distSC)*sgn(py1-py3);
#declare az = -((massA*massB)/distSB)*sgn(pz1-pz2) -
((massA*massC)/distSC)*sgn(pz1-pz3);

#write (nextpos, "#declare vx1= ", str((vx1+ax), 0, -1), ";n")
#write (nextpos, "#declare vy1= ", str((vy1+ay), 0, -1), ";n")
#write (nextpos, "#declare vz1= ", str((vz1+az), 0, -1), ";nn")

/////////////////////////////////////////////////////////////////////ball B
#write (nextpos, "#declare px2= ", str((px2+vx2), 0, -1), ";n")
#write (nextpos, "#declare py2= ", str((py2+vy2), 0, -1), ";n")
#write (nextpos, "#declare pz2= ", str((pz2+vz2), 0, -1), ";nn")

#declare distSA = (px2-px1)*(px2-px1) + (py2-py1)*(py2-py1) +
(pz2-pz1)*(pz2-pz1);
#declare distSC = (px2-px3)*(px2-px3) + (py2-py3)*(py2-py3) +
(pz2-pz3)*(pz2-pz3);

#declare ax = -((massB*massA)/distSA)*sgn(px2-px1) -
((massB*massC)/distSC)*sgn(px2-px3);
#declare ay = -((massB*massA)/distSA)*sgn(py2-py1) -
((massB*massC)/distSC)*sgn(py2-py3);
#declare az = -((massB*massA)/distSA)*sgn(pz2-pz1) -
((massB*massC)/distSC)*sgn(pz2-pz3);

#write (nextpos, "#declare vx2= ", str((vx2+ax), 0, -1), ";n")
#write (nextpos, "#declare vy2= ", str((vy2+ay), 0, -1), ";n")
#write (nextpos, "#declare vz2= ", str((vz2+az), 0, -1), ";nn")

/////////////////////////////////////////////////////////////////////ball C
#write (nextpos, "#declare px3= ", str((px3+vx3), 0, -1), ";n")
#write (nextpos, "#declare py3= ", str((py3+vy3), 0, -1), ";n")
#write (nextpos, "#declare pz3= ", str((pz3+vz3), 0, -1), ";nn")

#declare distSB = (px3-px2)*(px3-px2) + (py3-py2)*(py3-py2) +
(pz3-pz2)*(pz3-pz2);
#declare distSA = (px3-px1)*(px3-px1) + (py3-py1)*(py3-py1) +
(pz3-pz1)*(pz3-pz1);

#declare ax = -((massC*massB)/distSB)*sgn(px3-px2) -
((massC*massA)/distSA)*sgn(px3-px1);
#declare ay = -((massC*massB)/distSB)*sgn(py3-py2) -
((massC*massA)/distSA)*sgn(py3-py1);
#declare az = -((massC*massB)/distSB)*sgn(pz3-pz2) -
((massC*massA)/distSA)*sgn(pz3-pz1);

#write (nextpos, "#declare vx3= ", str((vx3+ax), 0, -1), ";n")
#write (nextpos, "#declare vy3= ", str((vy3+ay), 0, -1), ";n")
#write (nextpos, "#declare vz3= ", str((vz3+az), 0, -1), ";nn")

#fclose nextpos
(end of file)

distS(X), if you haven't guessed, means distance squared.

Some of the starting parameters I used were:
#declare px1= 0;
#declare py1= 0;
#declare pz1= 0;

#declare vx1= 0;
#declare vy1= 0;
#declare vz1= 0;

#declare px2= 100;
#declare py2= 100;
#declare pz2= 100;

#declare vx2= -.3;
#declare vy2= 0;
#declare vz2= 0;

#declare px3= 0;
#declare py3= 0;
#declare pz3= 8;

#declare vx3= .2;
#declare vy3= 0;
#declare vz3= 0;
(end of file)

and

#declare px1= -3;
#declare py1= 0;
#declare pz1= 3;

#declare vx1= 0;
#declare vy1= 0;
#declare vz1= -.3;

#declare px2= 0;
#declare py2= 0;
#declare pz2= 0;

#declare vx2= 0;
#declare vy2= 0;
#declare vz2= .3;

#declare px3= 3;
#declare py3= 0;
#declare pz3= 3;

#declare vx3= .3;
#declare vy3= 0;
#declare vz3= 0;
(end of file)

PS: Does anybody know how to do formatting in this message board thing?

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