Variable-mass system the momentum of the system varies for Therefore, by Newton's second law Noting that u - v is the velocity of d"m" relative to "m", symbolized as v, this final equation can be arranged as In a system where mass is being ejected or ablated from a main body, the derivation is slightly different. At time "t", let a mass "m" travel at a velocity v, meaning the initial momentum of the system is Since the main body will be losing mass, d"m" will be negative, meaning that at a time "t" + d"t" the momentum of the system becomes
Rigid body dynamics the rigid body. The velocity of the points R along their trajectories are where ω is the angular velocity vector of the body. Work is computed from the dot product of each force with the displacement of its point of contact If the trajectory of a rigid body is defined by a set of generalized coordinates "q", "j" = 1, ..., "m", then the virtual displacements δr are given by The virtual work of this system of forces acting on the body in terms of the generalized coordinates becomes or collecting the coefficients of δq For simplicity consider a trajectory