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.
On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems
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.
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Yunt, K. (February 14, 2014). "On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems." ASME. J. Comput. Nonlinear Dynam. July 2014; 9(3): 031017. https://doi.org/10.1115/1.4026122
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