01-275 L. Bruneau, S. DeBievre

A Hamiltonian model for linear friction in a homogeneous medium (548K, postscript) Jul 17, 01

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Abstract. We introduce and study rigorously a Hamiltonian model of a classical particle moving through a homogeneous dissipative medium at zero temperature in such a way that it experiences an effective {\em linear} friction force proportional to its velocity (at small speeds). The medium consists at each point in space of a vibration field modelling an obstacle with which the particle exchanges energy and momentum in such a way that total energy and momentum are conserved. We show that in the presence of a constant (not too large) external force, the particle reaches an asymptotic velocity proportional to this force. In a potential well, on the other hand, the particle comes exponentially fast to rest in the bottom of the well. The exponential rate is in both cases an explicit function of the model parameters and independent of the potential. We furthermore analyse in some detail the relation of our model to other models for dissipation that have been studied in the literature and derive in a simple manner a necessary condition for linear friction that has a straightforward physical interpretation.

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