Explicit, multi-map symplectic integrator for three-body classical trajectory studies in hyperspherical coordinates

Symplectic integrators are well known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary even order for separable Hamiltonians where the position and momentum coordinates are uncoupled. Explicit symplectic integrators for general Hamiltonians are more difficult to obtain, but can be developed by a composition of symplectic maps if the Hamiltonian can be split into exactly integrable parts. No general technique exists for splitting any Hamiltonian of general form. Many three body problems in classical mechanics can be effectively investigated in symmetrized, hyperspherical polar coordinates, but the Hamiltonian expressed in these coordinates is non-separable. In molecular dynamics, the hyperspherical coordinates facilitate the validation and visualization of potential energy surfaces and for quantum reactive scattering problems, the coordinates eliminate the need for adjusting the wavefunction between product and reactant channels. An explicit symplectic integrator for hyperspherical coordinates has not yet been devised. This dissertation presents an explicit, multi-map symmetrized composition method symplectic integrator for three-body Hamiltonians in symmetrized, hyperspherical polar coordinates, specifically for classical trajectory studies in the plane.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemistry

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Burkhardt, Paul

Contributors dc:contributor

• Belford, R. Linn
• Martinez, Todd J.
• McDonald, J. Douglas

• Chemistry
• Symplectic integrator
• Three-body classical trajectory
• Hyperspherical coordinates
• Classical mechanics
• Hamiltonian dynamics

Statement dc:rights

• Copyright 2004 Paul Burkhardt

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/17345

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/17345