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On the Relation of the Principle of Maximum Dissipation to the Principle of Gauss

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

Abstract: The aim of this work is to establish the relation between two well-known principles of dynamics for finite-dimensional Lagrangian systems subject to non-impulsive dissipative force laws. These two principles are the principle of maximum dissipation (PMD) and the principle of Gauss. For dynamics, where the evolution requires the determination of the accelerations of the system, it is shown that in the presence of dissipative force laws a similar principle holds, which requires the augmentation of the optimization problem of least constraints by the time rate of total dissipation. The dual problem of least constraints is derived from the maximization of the total time derivative of the total dissipation with respect to passive dissipative forces.

Keywords: Quadratic Programming, Variational Inequalities, Nonsmooth Analysis, Dissipative Systems

Category 1: Applications -- Science and Engineering (Basic Sciences Applications )

Category 2: Convex and Nonsmooth Optimization

Category 3: Complementarity and Variational Inequalities

Citation: Submitted to the Journal of Computational and Nonlinear Dynamics on 8th Nov. 2011

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Entry Submitted: 01/05/2012
Entry Accepted: 01/05/2012
Entry Last Modified: 11/15/2013

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