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Discrete nonholonomic LL systems on Lie groups
Fedorov, Yuri; Zenkov, Dmitry
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.
Dynamics
Hamiltonian dynamical systems
Lagrangian functions
Differentiable dynamical systems
Lie groups
Partícules (Física nuclear)
Hamilton, Sistemes de
Lagrange, Funcions de
Sistemes dinàmics diferenciables
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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