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N-body problem (3).gif

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N-body_problem_(3).gif(264 × 232 pixels, file size: 1.96 MB, MIME type: image/gif)

Summary Edit

The chaotic movement of 3 interacting particles.

This is an animation of the (not-reduced) three-body problem. The center of view is the mass center of the three particles.

Calculated numerically with Maple 10. Note: the 'n' parameter (currently '3') can be adapted at will.

> restart;with(RandomTools);with(plottools):with(plots);
> n:=8;
> e:={}:for i from 1 to n do
   s:=[]:for c from 1 to n do;  if (not(c=i)) then
   s:=[op(s),G*mass[i]*mass[c]*(x[c](t)-x[i](t))/sqrt(((x[c](t)- x[i](t))^2+(y[c](t)-y[i](t))^2+(z[c](t)-z[i](t))^2))^3]: end if od:
   e:={op(e),mass[i]*diff(x[i](t),t$2)=add(s[v],v=1..n-1)}:
  
   s:=[]:for c from 1 to n do;  if (not(c=i)) then
   s:=[op(s),G*mass[i]*mass[c]*(y[c](t)-y[i](t))/sqrt(((x[c](t)- x[i](t))^2+(y[c](t)-y[i](t))^2+(z[c](t)-z[i](t))^2))^3]: end if od:
   e:={op(e),mass[i]*diff(y[i](t),t$2)=add(s[v],v=1..n-1)}:
  
   s:=[]:for c from 1 to n do;  if (not(c=i)) then
   s:=[op(s),G*mass[i]*mass[c]*(z[c](t)-z[i](t))/sqrt(((x[c](t)- x[i](t))^2+(y[c](t)-y[i](t))^2+(z[c](t)-z[i](t))^2))^3]: end if od:
   e:={op(e),mass[i]*diff(z[i](t),t$2)=add(s[v],v=1..n-1)}:
  od:e;
> G:=200;
> SetState(state=12);
> pos:=[]:for i from 1 to n do pos:=[op(pos),Generate(list(integer(range=-10..10), 3))] od;
> vel:=[]:for i from 1 to n do vel:=[op(vel),Generate(list(integer(range=-5..5), 3))] od;
> mass:=Generate(list(integer(range=5..35), n));
> with(LinearAlgebra):
> beginvwn:=NULL:
   for i from 1 to n do beginvwn:=beginvwn,x[i](0)=pos[i][1],y[i](0)=pos[i][2],z[i](0)=pos[i][3] od:
   for i from 1 to n do beginvwn:=beginvwn,D(x[i])(0)=vel[i][1],D(y[i])(0)=vel[i][2],D(z[i])(0)=vel[i][3] od:
  beginvwn;
> var:=NULL:for i from 1 to n do var:=var,x[i](t),y[i](t),z[i](t) od:var;
> astappen:=500:timescale:=0.02:
  opl:=dsolve([op(e),beginvwn],numeric,output=array([seq(m*timescale,m=0..astappen-1)]),maxfun=500000):
> sl:=convert(opl[1,1],list);
> dp:=ListTools[Flatten]([seq([2+2*k,2+2*k+2*n,2+2*k+4*n],k=0..n-1)]);
> data:=convert(opl[2,1],listlist):
> mc:=[seq(map(list->sum(list[dp[cd+3*cs]]*mass[cs+1],cs=0..n-1)/sum(mass[cs],cs=1..n),data),cd=1..3)]:
> aschijfjes:=astappen;p:=[]:
  for k from 1 to aschijfjes do
  pts:=NULL:for i from 1 to n do pts:=pts,point([seq(data[k][dp[c+3*(i-1)]],c=1..3)],symbolsize=mass[i],color=red,symbol=DIAMOND) od:
  pp:=display(pts);
  p:=[op(p),pp];
  end do:
> display(p,insequence=true,scaling=constrained,axes=boxed);
> aschijfjes:=astappen;p:=[]:
  for k from 1 to aschijfjes do
  pts:=NULL:for i from 1 to n do pts:=pts,point([seq(mc[c][k]-data[k][dp[c+3*(i-1)]],c=1..3)],symbolsize=mass[i],color=red,symbol=DIAMOND) od:
  pp:=display(pts);
  p:=[op(p),pp];
  end do:
> display(p,insequence=true,scaling=constrained,axes=boxed);

Licensing Edit

PD-icon I, the author of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


This page uses content from the Wikimedia Commons. The original content was at File:N-body problem (3).gif. The list of authors can be seen in the page history. As with this Psychology Wiki wiki, that portion of the content of Wikimedia Commons is available under the GNU Free Documentation License.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current23:41, November 4, 2007Thumbnail for version as of 23:41, November 4, 2007264 × 232 (1.96 MB)PhloxBot (Talk | contribs)== Summary == The chaotic movement of 3 interacting particles. This is an animation of the (not-reduced) three-body problem. The center of view is the mass center of the three particles. Calculated numerically with Maple 10. Note: the 'n' parameter (cur

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