Relativistic angular momentum can be compactly abbreviated in tensor index notation where the indices "i" and "j" take the values 1, 2, 3. On the other hand, the components can be systematically displayed fully in a 3 × 3 antisymmetric matrix This quantity is additive, and for an isolated system, the total angular momentum of a system is conserved. In classical mechanics, the three-dimensional quantity for a particle of mass "m" moving with velocity u has the dimensions of "mass moment" – length multiplied by mass. It is related to the boost (relative velocity) of the centre of mass (COM) of the particle
Zero-velocity surface Zero-velocity surface The zero-velocity surface is a concept that relates to the N-body problem of gravity. It represents a surface a body of given energy cannot cross, since it would have zero velocity on the surface. It was first introduced by George William Hill. The zero-velocity surface is particularly significant when working with weak gravitational interactions among orbiting bodies. In the circular restricted three-body problem two heavy masses orbit each other at constant radial distance and angular velocity, and a particle of negligible mass is affected by their gravity. By shifting to a rotating coordinate system where the masses are