Center of mass separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system. The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is an inertial frame in which the center of mass of a system is at
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