On the lagrangian formalism of nonholonomic mechanical systems

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    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 publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
    Pages627-633
    Number of pages7
    Volume6 A
    Publication statusPublished - 2005
    EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA
    Duration: 2005 Sep 242005 Sep 28

    Other

    OtherDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
    CityLong Beach, CA
    Period05/9/2405/9/28

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    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    Yoshimura, H. (2005). On the lagrangian formalism of nonholonomic mechanical systems. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005 (Vol. 6 A, pp. 627-633)