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Research Papers

On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems

[+] Author and Article Information
Kerim Yunt

am Holbrig 4,
Zurich 8049, Switzerland
e-mail: kerimyunt@web.de

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received July 4, 2013; final manuscript received November 22, 2013; published online February 14, 2014. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 9(3), 031017 (Feb 14, 2014) (11 pages) Paper No: CND-13-1168; doi: 10.1115/1.4026122 History: Received July 04, 2013; Revised November 22, 2013

A dissipation based definition of the principle of Jourdain is presented for rheonomic (explicitly time dependent) mechanical systems, which evolve under the influence of convex dissipation potentials. It is shown, that the variational condition of the dissipative principle of Jourdain is the necessary condition for the maximization of the total dissipated power with respect to generalized velocities. The principle of maximum dissipation is shown to be the dual principle of the dissipative principle of Jourdain. A dissipative principle of Gauss is formulated by making use of nonsmooth analysis and potential theory and its dual principle is formulated.

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Figures

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Fig. 2

In one dimension: (a) The absolute value function and its subdifferential; (b) conjugate of the Euclidean distance function to the origin; and (c) the subdifferential of Ψ[-1,1](x) and |y| in comparison

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Fig. 3

The spatial frictional disc Ct(fn) with normal force dependent radius and various normal cones (red)

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Fig. 4

The geometry of a single spatial rigid body contact between two rigid bodies

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Fig. 5

Three boxes moving on a frictional ground

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Fig. 6

Free body diagram with various forces

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