On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints

Hiroaki Yoshimura, Kenji Soya

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

    1 Citation (Scopus)

    Abstract

    This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear-Gupta-Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.

    Original languageEnglish
    Title of host publicationProceedings of the ASME Design Engineering Technical Conference
    Pages517-521
    Number of pages5
    Volume4
    EditionPARTS A, B AND C
    DOIs
    Publication statusPublished - 2009
    EventASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009 - San Diego, CA
    Duration: 2009 Aug 302009 Sep 2

    Other

    OtherASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009
    CitySan Diego, CA
    Period09/8/3009/9/2

    Fingerprint

    Discrete Hamiltonian System
    Hamiltonians
    Stabilization
    Geometric Constraints
    Hamiltonian Systems
    Backward Differentiation Formula
    Symplectic Structure
    Constrained Systems
    Mechanical Systems
    Linkage
    Gears
    Discretization

    ASJC Scopus subject areas

    • Mechanical Engineering
    • Computer Graphics and Computer-Aided Design
    • Computer Science Applications
    • Modelling and Simulation

    Cite this

    Yoshimura, H., & Soya, K. (2009). On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. In Proceedings of the ASME Design Engineering Technical Conference (PARTS A, B AND C ed., Vol. 4, pp. 517-521) https://doi.org/10.1115/DETC2009-86354

    On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. / Yoshimura, Hiroaki; Soya, Kenji.

    Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A, B AND C. ed. 2009. p. 517-521.

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

    Yoshimura, H & Soya, K 2009, On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. in Proceedings of the ASME Design Engineering Technical Conference. PARTS A, B AND C edn, vol. 4, pp. 517-521, ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009, San Diego, CA, 09/8/30. https://doi.org/10.1115/DETC2009-86354
    Yoshimura H, Soya K. On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. In Proceedings of the ASME Design Engineering Technical Conference. PARTS A, B AND C ed. Vol. 4. 2009. p. 517-521 https://doi.org/10.1115/DETC2009-86354
    Yoshimura, Hiroaki ; Soya, Kenji. / On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A, B AND C. ed. 2009. pp. 517-521
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