Exact discrete Lagrangian mechanics for nonholonomic mechanics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Apr 2022Embargo end date: 01 Jan 2020 Spain English Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 151, pages 49-98 (issn: 0029-599X, eissn: 0945-3245,

Copyright policy )Funded by:FCT | Análise Geométrica e Numé...

Authors: Alexandre Anahory Simoes; Juan Carlos Marrero; David Martín de Diego;

doi: 10.1007/s00211-022-01283-2 , 10.48550/arxiv.2003.11362

arXiv: 2003.11362

handle: 10261/273208

Exact discrete Lagrangian mechanics for nonholonomic mechanics

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Abstract

AbstractWe construct the exponential map associated to a nonholonomic system that allows us to define an exact discrete nonholonomic constraint submanifold. We reproduce the continuous nonholonomic flow as a discrete flow on this discrete constraint submanifold deriving an exact discrete version of the nonholonomic equations. Finally, we derive a general family of nonholonomic integrators that includes as a particular case the exact discrete nonholonomic trajectory.

Country

Spain

Related Organizations

University of La Laguna
Spain
Universidad de La Laguna (ULL)
Spain
Spanish National Research Council
Spain
Institute of Mathematical Sciences
Spain

Keywords

Mathematics - Differential Geometry, Constrained dynamics, Dirac's theory of constraints, 34C25, 37E40, 70K40, Nonholonomic systems related to the dynamics of a system of particles, FOS: Physical sciences, Mathematical Physics (math-ph), Numerical Analysis (math.NA), Numerical methods for Hamiltonian systems including symplectic integrators, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, Differential Geometry (math.DG), Numerical integration, FOS: Mathematics, Mathematics - Numerical Analysis, Mathematical Physics

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