Criterion for Stability of a Special Relativistically Covariant Dynamical System
Classical Physics
2017-04-05 v1 Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincar'e plots of the simulated motion are consistent with the RGEM. We found a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.
Keywords
Cite
@article{arxiv.1704.00811,
title = {Criterion for Stability of a Special Relativistically Covariant Dynamical System},
author = {L. P Horwitz and D. Zucker},
journal= {arXiv preprint arXiv:1704.00811},
year = {2017}
}
Comments
11 pages. 18 figures