Geometric Generalisations of Shake and Rattle
Artikel i vetenskaplig tidskrift, 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.

Författare

Robert I McLachlan

Massey University

Klas Modin

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Olivier Verdier

Norges teknisk-naturvitenskapelige universitet

Matt Wilkins

Massey University

Foundations of Computational Mathematics

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

Vol. 14 2 339-370

Fundament

Grundläggande vetenskaper

Ämneskategorier

Geometri

DOI

10.1007/s10208-013-9163-y