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March  2010, 3(1): 105-128. doi: 10.3934/dcdss.2010.3.105

Variational constrained mechanics on Lie affgebroids

Juan Carlos Marrero 1, , D. Martín de Diego 2, and  Diana Sosa 3,

1. 

Unidad Asociada ULL-CSIC "Geometría Diferencial y Mecánica Geométrica", Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain
2. 

Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid, Spain
3. 

Departamento de Economía Aplicada y Unidad Asociada ULL-CSIC, "Geometría Diferencial y Mecánica Geométrica," Facultad de CC. EE. y Empresariales, Universidad de La Laguna, and Universidad Europea de Canarias, Calle de Inocencio García 1, La Orotava, Tenerife, Canary Islands, Spain

Received  September 2008 Revised  January 2009 Published  December 2009

In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid $\mathcal A$. We devote special attention to the particular case when the nonholonomic constraints are given by an affine subbundle of $\mathcal A$ and we discuss the variational character of the theory. Finally, we apply the results obtained to several examples.
Keywords: Lie affgebroids, constraint algorithm, Hamiltonian Mechanics, Lagrangian Mechanics, time-dependent mechanics, variational calculus., vakonomic mechanics, affine constraints, aff-Poisson brackets, AV-bundles, Lie algebroids.
Mathematics Subject Classification: 17B66, 37J60, 70F25, 70G45, 70G75, 70H3.
Citation: Juan Carlos Marrero, D. Martín de Diego, Diana Sosa. Variational constrained mechanics on Lie affgebroids. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 105-128. doi: 10.3934/dcdss.2010.3.105
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