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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