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Título : A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
Autor : Iglesias, David; Marrero, Juan Carlos; Martín de Diego, David; Sosa, Diana
Palabras clave : Lie algebroids
Lie affgebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic Mechanics
Lagrange-d’Alembert equations
Projectors
AV-bundles
Aff-Poisson brackets
Non-holonomic brackets
Fecha de publicación : 2-may-2007
Editor: American Institute of Physics
Citación : arXiv:0705.0278v1
Journal of Mathematical Physics 48(8): 083513 (2007)
Resumen: This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems.
Descripción : 50 pages.-- Pre-print archive.-- PACS: 45.05.+x; 02.20.Sv; 02.40.Hw
Versión del editor: http://dx.doi.org/10.1063/1.2776845
URI : http://hdl.handle.net/10261/2281
DOI: 10.1063/1.2776845
ISSN: 0022-2488
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