Nonlinear constraints in nonholonomic mechanics

Paul Popescu; Cristian Ida

doi:10.3934/jgm.2014.6.527

Article Contents

2014, Volume 6, Issue 4: 527-547. Doi: 10.3934/jgm.2014.6.527

This issue Previous Article Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings Next Article A dynamical condition for differentiability of Mather's average action

Nonlinear constraints in nonholonomic mechanics

Paul Popescu^1, and
Cristian Ida^2,

1.
Department of Applied Mathematics, University of Craiova, Craiova 200585, Str. A.I. Cuza 13
2.
Department of Mathematics and Informatics, University Transilvania of Braşov, Braşov 500091, Str. Iuliu Maniu 50

Received: November 30, 2013

Revised: May 31, 2014

Published: November 2014

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Abstract

In this paper we have obtained some dynamics equations, in the presence of nonlinear nonholonomic constraints and according to a lagrangian and some Chetaev-like conditions. Using some natural regular conditions, a simple form of these equations is given. In the particular cases of linear and affine constraints, one recovers the classical equations in the forms known previously, for example, by Bloch and all [3,4]. The case of time-dependent constraints is also considered. Examples of linear constraints, time independent and time depenndent nonlinear constraints are considered, as well as their dynamics given by suitable lagrangians. All examples are based on classical ones, such as those given by Appell's machine.

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Mathematics Subject Classification: Primary: 70F25, 37J60, 70H45; Secondary: 37C99.

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