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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Symplectic integration of constrained Hamiltonian systems
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by B. Leimkuhler and S. Reich PDF
Math. Comp. 63 (1994), 589-605 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 589-605
  • MSC: Primary 65L05; Secondary 34A50, 58F05, 70-08, 70H05
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1250772-7
  • MathSciNet review: 1250772