Variational constrained mechanics on Lie affgebroids

Abstract

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 A. We devote special attention to the particular case when the nonholonomic constraints are given by an affine subbundle of A and we discuss the variational character of the theory. Finally, we apply the results obtained to several examples.