Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

Abstract

The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon–Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space.

Document Details

Document Type
Pub Defense Publication
Publication Date
Dec 30, 2017
Source ID
10.1142/s021812741750225x

Entities

People

  • Atanasiu Stefan Demian
  • Stephen Wiggins

Organizations

  • Engineering and Physical Sciences Research Council
  • Office of Naval Research
  • University of Bristol

Tags

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Quantum Chemistry
  • Robotics and Automation.

Technology Areas

  • Space