CaltechAUTHORS
  A Caltech Library Service

Symplectic reduction and topology for applications in classical molecular dynamics

Lin, F. J. and Marsden, J. E. (1992) Symplectic reduction and topology for applications in classical molecular dynamics. Journal of Mathematical Physics, 33 (4). pp. 1281-1294. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:LINjmp92

[img]
Preview
PDF - Published Version
See Usage Policy.

1395Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:LINjmp92

Abstract

This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate system to the center of mass coordinate system relevant to molecular collision dynamics. For the case of two-body molecular systems constrained to a plane, symplectic reduction is employed to demonstrate explicitly the separation of translational, rotational, and internal energies and the corresponding reductions of the phase space describing the dynamics for Hamiltonian systems with symmetry. Further, by examining the topology of the energy-momentum map, a unified treatment is presented of the reduction results for the description of (i) the classical dynamics of rotating and vibrating diatomic molecules, which correspond to bound trajectories and (ii) the classical dynamics of atom–atom collisions, which correspond to scattering trajectories. This provides a framework for the treatment of the dynamics of larger N-body systems, including the dynamics of larger rotating and vibrating polyatomic molecular systems and the dynamics of molecule–molecule collisions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.529705DOIUNSPECIFIED
http://link.aip.org/link/?JMAPAQ/33/1281/1PublisherUNSPECIFIED
Additional Information:Copyright © 1992 American Institute of Physics. Received 16 October 1991; accepted 21 November 1991.
Subject Keywords:TOPOLOGY, MANY−BODY PROBLEM, MOLECULE COLLISIONS, PHASE SPACE, CENTER−OF−MASS SYSTEM, VIBRATIONAL STATES, ROTATIONAL STATES, ATOM−ATOM COLLISIONS, POLYATOMIC MOLECULES, HAMILTONIAN FUNCTION, DIFFERENTIAL CROSS SECTIONS, TWO−BODY PROBLEM, SCATTERING, VAN DER WAALS FORCES, TRAJECTORIES, CLASSICAL MECHANICS, DIATOMIC MOLECULES, MOLECULAR DYNAMICS CALCULATIONS, INTERNAL ENERGY
Record Number:CaltechAUTHORS:LINjmp92
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LINjmp92
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13026
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:15 Jan 2009 23:06
Last Modified:26 Dec 2012 10:43

Repository Staff Only: item control page