Haven't got space for conservation
Classical Mechanics
Level
2
Consider a system of \(N\) particles whose coordinates are \(\{r_i\}\), and whose velocities are \(\{\dot{r}_i\}\). Each pair of particles \(\left(i, j\right)\) interacts through a potential \(V_{ij}\left(r_i, r_j\right)\) which depends on the coordinates \(\left(r_i, r_j\right)\) only through their difference, i.e. \[V_{ij}\left(r_i, r_j, t\right) = V_{ij}\left(r_i-r_j, t\right)\] As the system evolves in time, which of the following bulk quantities must be conserved?
by
Josh Silverman