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.
|Author:||Benedict Leimkuhler, Sebastian Reich|
|Series (Serial Number):||Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, ISSN 1866-8372 (paper 032)|
|Date of Publication (online):||2007/11/16|
|Year of Completion:||1994|
|Publishing Institution:||Universität Potsdam|
|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|
ﬁrst published in:
Mathematics of Computation - 63 (1994), 208, p. 589 - 605
Published by the American Mathematical Society.