Relative motion in spacetime
Abstract
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The issue of an equivalent one-body description is discussed. We distinguish two different concepts: on the one hand an almost purely kinematic relative particle, on the other hand an effective particle which involves an explicit dynamical formulation; several versions of the latter are possible. Relative and effective particles have the same orbit, but may differ by their schedules.
Cite
@article{arxiv.1309.4313,
title = {Relative motion in spacetime},
author = {Philippe Droz-Vincent},
journal= {arXiv preprint arXiv:1309.4313},
year = {2015}
}
Comments
26 pages, no figure. Several inadequacies and various misprints corrected. An example, an Appendix, one reference added; some obscure points clarified