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This paper concerns an intrinsic formulation of nonholonomic mechanics. Our point of departure is the paper [6], by Koiller et al., revisiting E. Cartan's address at the International Congress of Mathematics held in 1928 at Bologna, Italy ([3]). Two notions of equivalence for nonholonomic mechanical systems (M, g, D) are introduced and studied. According to [6], the notions of equivalence considered in this paper coincide. A counterexample is presented here showing that this coincidence is not always true.

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We study a version of the inverse problem of Calculus of Variations in the context of Vakonomic Mechanics.

We study a version of the inverse problem of Calculus of Variations in the context of Vakonomic Mechanics.

Abstract. We present conditions for hyperbolicity and existence of an invariant measure for the GMA flow of a non-linearly constrained mechanical system. The conservation of volume in the linear constrained problem corresponding to the rolling of a ball on a surface parallel to Delaunay is also considered.

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