Consider a system with N particles whose coordinates are ri={rix,riy,riz}, and whose velocities are r˙i. The energy of the system is described by the kinetic energy 21m∑r˙2 and an effective potential energy term V(r1,…,rN).
All we know about V is that it depends on the positions only through their differences r1−r2, i.e.
V({ri},t)=V(r1−r2,r1−r3,…,t).
As this system evolves in time, which of the following bulk quantities must be conserved?
Assumptions
- All interactions of the system with the outside world are described by V.