1. when I have systems with 3 mass points ($m_i, i=1,2,3$) to a time $t=t_0$ on positions $\vec r_i(t_0)$ and velocity $\vec v_i(t_0)$. How could a syntax look like to calculate

1) center of mass 2) total momentum 3) total angular momentum

for any number of mass points?

  1. Secondly, later when time is $t_1 > t_0$ the positions and velocities of 2 of this 3 mass poins are known. How could mathematica calculate position and velocity of third mass point, when there is no external force ?

Thank you very much!


Center of mass:

Total[m1 r1, m2 r2, m3 r3]/Total[m1,m2,m3]

Total momentum:

Total[m1 v1, m2 v2, m3 v3]

Total angular momentum:

Total[m1 Cross[r1,v1], m2 Cross[r2,v2], m3 Cross[r3,v3]]
  • $\begingroup$ thanx so far david! $\endgroup$ – Tom Jan 12 at 20:44

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