TITLE:
Reaction Mechanics for Point Objects
AUTHORS:
Philipp Kornreich
KEYWORDS:
Lagrangian, Hamiltonian, Poisson Bracket, Variational Method, Propagation Delay, Causal, Classical Mechanics, General Theory of Relativity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.1,
January
25,
2017
ABSTRACT: The least action principle is used to derive a general mathematical model of the motion of point objects subject to non-instantaneous interactions. A Lagrangian Equation of Motion, a Hamiltonian Formalism, a Poisson Bracket and the Relation of Reaction Mechanics and the General Theory of Relativity are derived here. In the limit of no delay, the equation of motion reverts to Newtonian Mechanics. In the limit of infinitesimal delay, the equation of motion takes the form of the Geodesic Equation of Motion of the General Theory of Relativity. For two objects, the single instantaneous interaction splits into two interactions when the propagation delay is considered. Object ONE experiences the following interactions at the present: it senses an interaction radiated by object TWO in the past. It also radiates an interaction that other objects might or might not sense in the future. It experiences a Recoil interaction equal in magnitude and opposed to the direction of the interaction it radiated. The Recoil interaction is independent of the radiated interaction reaching its target or not reaching its target. The Recoil interaction is causal.