# center of mass system, momentum

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]]

• thanx so far david! – Tom Jan 12 at 20:44