Improving E. Cartan considerations on the invariance of nonholonomic mechanics

Waldyr M. Oliva; Gláucio Terra

doi:10.3934/jgm.2019022

Article Contents

2019, Volume 11, Issue 3: 439-446. Doi: 10.3934/jgm.2019022

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Improving E. Cartan considerations on the invariance of nonholonomic mechanics

Waldyr M. Oliva^1,2, and
Gláucio Terra^3,

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

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Abstract

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.

Keywords:

Nonholonomic systems,
Cartan's equivalence method.

Mathematics Subject Classification: Primary: 37J60, 70F25; Secondary: 70G45.

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References

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