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Hamilton's Principle as Variational Inequality forMechanical Systems with Impact

Leine, R. ; Aeberhard, U. ; Glocker, C.

In: Journal of Nonlinear Science, 2009, vol. 19, no. 6, p. 633-664

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    Titre
    • Hamilton's Principle as Variational Inequality forMechanical Systems with Impact
    Auteur
    • Leine, R.. Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, 8092, Zurich, Switzerland
    • Aeberhard, U.. Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, 8092, Zurich, Switzerland
    • Glocker, C.. Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, 8092, Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Nonlinear Science, 2009, vol. 19, no. 6, p. 633-664. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319609
    Summary
    The classical form of Hamilton's principle holds for conservative systems with perfect bilateral constraints. Several attempts have been made in literature to generalise Hamilton's principle for mechanical systems with perfect unilateral constraints involving impulsive motion. This has led to a number of different variants of Hamilton's principle, some expressed as variational inequalities. Up to now, the connection between these different principles has been missing. The aim of this paper is to put these different principles of Hamilton in a unified framework by using the concept of weak and strong extrema. The difference between weak and strong variations of the motion is explained in detail. Each type of variation leads to a variant of the principle of Hamilton in the form of a variational inequality. The conclusion of the paper is that each type of variation leads to different necessary and sufficient conditions on the impact law. The principle of Hamilton with strong variations is valid for perfect unilateral constraints with a completely elastic impact law, whereas the weak form of Hamilton's principle only requires perfect unilateral constraints and no condition on the energy