Geometric Generalisations of Shake and Rattle
Journal article, 2014

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises shake and rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for Shake and Rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given.


Robert I McLachlan

Massey University

Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Olivier Verdier

Norwegian University of Science and Technology (NTNU)

Matt Wilkins

Massey University

Foundations of Computational Mathematics

1615-3375 (ISSN) 1615-3383 (eISSN)

Vol. 14 2 339-370


Basic sciences

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