# American Institute of Mathematical Sciences

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

## Variational constrained mechanics on Lie affgebroids

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.
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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