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The Principle of Hamilton for Mechanical Systems with Impacts and Unilateral Constraints

Kerim Yunt Yunt(kerimyunt***at***web.de)

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. The energetical behavior for elastic, plastic and blocking type impacts are 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 behaviour which conforms with the physics of the impactive process, is shown to be the consistency conditions on the impact time variations.

Keywords: principle of Hamilton, variational calculus, stationary principle, impact mechanics

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Journal of Nonlinear Science JNLS-D-14-00106 submitted., 10.5.2014

Download: [PDF]

Entry Submitted: 07/27/2014
Entry Accepted: 07/27/2014
Entry Last Modified: 07/27/2014

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