Hamilton-Pontryagin principle for incompressible ideal fluids

Hiroaki Yoshimura, François Gay-Balmaz

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

    Abstract

    We develop the Hamilton-Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler-Poincaré equations with advective parameters. Then, we derive the reduced Hamilton-Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton-Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler-Poincaré equations.

    Original languageEnglish
    Title of host publicationAIP Conference Proceedings
    Pages645-647
    Number of pages3
    Volume1376
    DOIs
    Publication statusPublished - 2011
    EventProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI - Guangzhou
    Duration: 2011 Jun 302011 Jul 3

    Other

    OtherProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI
    CityGuangzhou
    Period11/6/3011/7/3

    Fingerprint

    pontryagin principle
    ideal fluids
    Lagrange multipliers
    preserving
    analogs
    momentum
    configurations

    Keywords

    • Advective Parameters
    • Hamilton-Pontryagin Principle
    • Implicit Euler-Poincaré Equations

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Yoshimura, H., & Gay-Balmaz, F. (2011). Hamilton-Pontryagin principle for incompressible ideal fluids. In AIP Conference Proceedings (Vol. 1376, pp. 645-647) https://doi.org/10.1063/1.3652002

    Hamilton-Pontryagin principle for incompressible ideal fluids. / Yoshimura, Hiroaki; Gay-Balmaz, François.

    AIP Conference Proceedings. Vol. 1376 2011. p. 645-647.

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

    Yoshimura, H & Gay-Balmaz, F 2011, Hamilton-Pontryagin principle for incompressible ideal fluids. in AIP Conference Proceedings. vol. 1376, pp. 645-647, Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI, Guangzhou, 11/6/30. https://doi.org/10.1063/1.3652002
    Yoshimura H, Gay-Balmaz F. Hamilton-Pontryagin principle for incompressible ideal fluids. In AIP Conference Proceedings. Vol. 1376. 2011. p. 645-647 https://doi.org/10.1063/1.3652002
    Yoshimura, Hiroaki ; Gay-Balmaz, François. / Hamilton-Pontryagin principle for incompressible ideal fluids. AIP Conference Proceedings. Vol. 1376 2011. pp. 645-647
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