# American Institute of Mathematical Sciences

September  2019, 11(3): 439-446. doi: 10.3934/jgm.2019022

## Improving E. Cartan considerations on the invariance of nonholonomic mechanics

 1 Universidade de Lisboa, Instituto Superior Técnico, Center for Mathematical Analysis, Geometry and Dynamical Systems, Av. Rovisco Pais, 1049-001 Lisbon, Portugal 2 Universidade de São Paulo, Instituto de Matemática e Estatística, Departamento de Matemática Aplicada, Rua do Matão, 1010, 05508-090 São Paulo, Brazil 3 Universidade de São Paulo, Instituto de Matemática e Estatística, Departamento de Matemática, Rua do Matão, 1010, 05508-090 São Paulo, Brazil

Received  February 2019 Published  August 2019

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

Citation: Waldyr M. Oliva, Gláucio Terra. Improving E. Cartan considerations on the invariance of nonholonomic mechanics. Journal of Geometric Mechanics, 2019, 11 (3) : 439-446. doi: 10.3934/jgm.2019022
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