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
Angular velocity which shows a connection with the Lie group of rotations. We prove that angular velocity tensor is skew symmetric, i.e. formula_63 satisfies formula_64. A rotation matrix "A" is orthogonal, inverse to its transpose, so we have formula_65. For formula_66 a frame matrix, taking the time derivative of the equation gives: Applying the formula formula_68, Thus, "W" is the negative of its transpose, which implies it is skew symmetric. At any instant formula_70, the angular velocity tensor represents a linear map between the position vector formula_71 and the velocity vectors formula_72 of a point on a rigid body rotating around the