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# Variational constrained mechanics on Lie affgebroids

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

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