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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Symplectic integration of constrained Hamiltonian systems


Authors: B. Leimkuhler and S. Reich
Journal: Math. Comp. 63 (1994), 589-605
MSC: Primary 65L05; Secondary 34A50, 58F05, 70-08, 70H05
MathSciNet review: 1250772
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Abstract | References | Similar Articles | Additional Information

Abstract: A Hamiltonian system in potential form $ (H(q,p) = {p^t}{M^{ - 1}}p/2 + F(q))$ subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in $ {{\mathbf{R}}^n}$. In this paper, methods which reduce "Hamiltonian differential-algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parametrizations 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1250772-7
PII: S 0025-5718(1994)1250772-7
Keywords: Differential-algebraic equations, constrained Hamiltonian systems, canonical discretization schemes, symplectic methods
Article copyright: © Copyright 1994 American Mathematical Society