On the lagrangian formalism of nonholonomic mechanical systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The paper Illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d'Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d'Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

Original languageEnglish
Title of host publicationProc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005
Subtitle of host publication5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
Pages627-633
Number of pages7
ISBN (Print)0791847438, 9780791847435
DOIs
Publication statusPublished - 2005
EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States
Duration: 2005 Sep 242005 Sep 28

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume6 A

Conference

ConferenceDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CityLong Beach, CA
Period05/9/2405/9/28

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Yoshimura, H. (2005). On the lagrangian formalism of nonholonomic mechanical systems. In Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (pp. 627-633). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 6 A). American Society of Mechanical Engineers. https://doi.org/10.1115/detc2005-84273