Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 01, 2019
- Source ID
- 10.1142/s0218127419501578
Entities
People
- Stephen Wiggins
- Vladimír Krajňák
Organizations
- Engineering and Physical Sciences Research Council
- Office of Naval Research
- University of Bristol