Center of mass reference point R are and If R is chosen as the center of mass these equations simplify to where "m" is the total mass of all the particles, p is the linear momentum, and L is the angular momentum The Law of Conservation of Momentum predicts that for any system not subjected to external forces the momentum of the system will remain constant, which means the center of mass will move with constant velocity. This applies for all systems with classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More formally, this is true for any
Derivation of the Navier–Stokes equations where it's assumed that all body forces are describable as gradients (for example it is true for gravity), and density has been divided so that viscosity becomes kinematic viscosity. The second vector calculus identity above states that the divergence of the curl of a vector field is zero. Since the (incompressible) mass continuity equation specifies the divergence of flow velocity being zero, we can replace the flow velocity with the curl of some vector formula_84 so that mass continuity is always satisfied: So, as long as flow velocity is represented through formula_86, mass continuity is unconditionally satisfied. With this new