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

Tags

Fields of Study

  • Mathematics
  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.