˜Theœ numerical solution of constrained Hamiltonian systems

Abstract: "A Hamiltonian system subject to smooth constraints can typically be viewed as a Hamiltonian system on a manifold. Numerical computations, however, must be performed in R[superscript n]. In this paper, canonical transformations from 'Hamiltonian differential-algebraic equations&#...

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Bibliographische Detailangaben
1. Verfasser: Leimkuhler, Benedict J. (VerfasserIn)
Weitere Verfasser: Reich, S. (VerfasserIn)
Format: UnknownFormat
Sprache:eng
Veröffentlicht: Berlin Konrad-Zuse-Zentrum für Informationstechnik 1992
Schriftenreihe:Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1992,16
Schlagworte:
Differential-algebraic equations > Hamiltonian systems
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Zusammenfassung:Abstract: "A Hamiltonian system subject to smooth constraints can typically be viewed as a Hamiltonian system on a manifold. Numerical computations, however, must be performed in R[superscript n]. In this paper, canonical transformations from 'Hamiltonian differential-algebraic equations' to ODEs in Euclidean space are considered. In [symbol]2, canonical parameterizations or local charts are developed and it is shown how these can be computed in a practical framework. In [symbol]3 we consider the construction of unconstrained Hamiltonian ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an integral invariant and whose flow reduces to the flow of the constrained system along the manifold
It is shown that certain of these unconstrained Hamiltonian systems force Lyapunov stability of the constraint-invariants, while others lead to an unstable invariant. In [symbol]4, we compare various projection techniques which might be incorporated to better insure preservation of the constraint-invariants in the context of numerical discretization. Numerical experiments illustrate the degree to which the constraint and symplectic invariants are maintained under discretization of various formulations.
Beschreibung:27 S.