Global modified Hamiltonian for constrained symplectic integrators

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Reference

Global modified Hamiltonian for constrained symplectic integrators

HAIRER, Ernst

Abstract

We prove that the numerical solution of partitioned Runge-Kutta methods applied to constrained Hamiltonian systems (e.g., the Rattle algorithm or the Lobatto IIIA--IIIB pair) is formally equal to the exact solution of a constrained Hamiltonian system with a globally defined modified Hamiltonian. This property is essential for a better understanding of their longtime behaviour. As an illustration, the equations of motion of an unsymmetric top are solved using a parameterization with Euler parameters.

HAIRER, Ernst. Global modified Hamiltonian for constrained symplectic integrators.

Numerische Mathematik , 2003, vol. 95, no. 2, p. 325-336

DOI : 10.1007/s00211-002-0428-7

Available at:

http://archive-ouverte.unige.ch/unige:12278

Disclaimer: layout of this document may differ from the published version.

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