Symplectic integration of constrained Hamiltonian systems

  • A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.

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Author:Benedict Leimkuhler, Sebastian Reich
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 032)
Document Type:Postprint
Date of Publication (online):2007/11/16
Year of Completion:1994
Publishing Institution:Universität Potsdam
Release Date:2007/11/16
Tag:canonical discretization schemes; constrained Hamiltonian systems; differential-algebraic equations; symplectic methods
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Notes extern:
first published in:
Mathematics of Computation - 63 (1994), 208, p. 589 - 605
ISSN: 0025-5718
Published by the American Mathematical Society.