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Título : Nonholonomic systems on Lie algebroids
Autor : Cortés, Jorge; León, Manuel de; Marrero, Juan Carlos; Martínez, Eduardo
Palabras clave : Nonholonomic Mechanics
Lagrange-d’Alembert equations
Lie algebroids
Symmetry
Reduction
Differential Geometry
Mathematical Physics
Fecha de publicación : 28-abr-2008
Editor: University of Missouri
Citación : arXiv:math-ph/0512003v3
Discrete and Continuous Dynamical Systems [in press]
Serie : DCDS-A-08
Resumen: This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. The proposed novel formalism provides new insights into the geometry of nonholonomic systems, and allows us to treat in a unified way a variety of situations, including systems with symmetry, morphisms and reduction, and nonlinearly constrained systems. Various examples illustrate the results.
Descripción : To appear in Discrete and Continuous Dynamical Systems A.-- 56 pages.-- 2000 MSC Classes: 70F25, 70H03, 70H33, 37J60, 53D17.
URI : http://hdl.handle.net/10261/4170
ISSN: 1078-0947
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