Criterion for stability of a special relativistically covariant dynamical system
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. Poincaré plots of the simulated motion are consistent with the RGEM. We find a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- March 2017
- DOI:
- 10.1088/1751-8121/aa59b7
- arXiv:
- arXiv:1704.00811
- Bibcode:
- 2017JPhA...50l5202H
- Keywords:
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- Physics - Classical Physics;
- Mathematical Physics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 11 pages. 18 figures