Improving E. Cartan considerations on the invariance of nonholonomic mechanics

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 \begin{document}$ ( {\mathsf{{M}}}, {{\mathsf{{g}}}}, {\mathscr{D}}) $\end{document} 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.