Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics
Dynamical Systems
2019-10-18 v1 Chaotic Dynamics
Abstract
We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.
Keywords
Cite
@article{arxiv.1905.04059,
title = {Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics},
author = {Vladimír Krajňák and Stephen Wiggins},
journal= {arXiv preprint arXiv:1905.04059},
year = {2019}
}