Variational constrained mechanics on Lie affgebroids

Juan Carlos Marrero; D. Martín de Diego; Diana Sosa

doi:10.3934/dcdss.2010.3.105

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2010, Volume 3, Issue 1: 105-128. Doi: 10.3934/dcdss.2010.3.105

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Variational constrained mechanics on Lie affgebroids

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
2.
Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid
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

Received: August 31, 2008

Revised: December 31, 2008

Published: February 2010

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Abstract

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.

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Mathematics Subject Classification: 17B66, 37J60, 70F25, 70G45, 70G75, 70H30.

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