Theoretical framework for particle dynamics in translational reference frames and application to multi-body dynamics

This article presents a systematic development of a new theoretical framework for particle dynamics in translational reference frames. Based on the symmetric new equation of particle dynamics, which effectively eliminates the dependence on the inertial reference frame, all classical mechanics theorems can be generalized in a form-invariant manner to any translational reference frame. This generalization necessitates redefining the force term: in particular, the total force (F|p) is replaced by the relative force (F|p−mpmoF|o), where F|o and mo represent the real force acting on and the mass of the reference particle. The advantages of this generalized theoretical framework are demonstrated through the derivation of planetary perturbation equations. In principle, the need for a center-of-mass reference frame is avoided. Furthermore, the direct application of the symmetric new equation enables a systematic integration of various additional perturbative forces into the modified planetary perturbation equations.