I have the velocity vectors and positions of n number of bodies in an N-Body system and I want to calculate the center of mass of the whole system.
Since I have the velocity vectors:
Let's say I find the definition of flat surfaces to which each velocity vectors are normal. Can I consider the intersection of all calculated surfaces as the center of mass of the system?
If yes,
How to calculate the definition of a flat surface which I know the definition of its normal vector?
What is the definition of a flat surface, if its normal vector is V(x, y, z)?
If not,
I am open to other suggestions for my original problem.