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The Hamilton Principle for Mechanical Systems with Impacts and Unilateral Constraints

In: Integral Methods in Science and Engineering

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  • K. Yunt

    (General Control Design)

Abstract

An action integral is presented for Hamiltonian mechanics in canonical form with unilateral constraints and/or impacts. The transition conditions on generalized impulses and the energy are presented as variational inequalities, which are obtained by the application of discontinuous transversality conditions. transversality conditions The energetical behavior for elastic, plastic, and blocking type impacts is analyzed. A general impact equation is obtained by the stationarity conditions, which is compatible with the most general impact laws and is applicable to various impactive processes straightforwardly. The crux in achieving energetical behavior which conforms with the physics of the impactive process is shown to be the consistency conditions on the impact time variations.

Suggested Citation

  • K. Yunt, 2015. "The Hamilton Principle for Mechanical Systems with Impacts and Unilateral Constraints," Springer Books, in: Christian Constanda & Andreas Kirsch (ed.), Integral Methods in Science and Engineering, edition 1, chapter 0, pages 687-699, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16727-5_57
    DOI: 10.1007/978-3-319-16727-5_57
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