A Hamiltonian Model for Linear Friction in a Homogeneous Medium |
| |
Authors: | Laurent Bruneau Stephan De Bièvre |
| |
Institution: | (1) UFR de Mathématiques et UMR AGAT, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France. E-mail: {bruneau; debievre}@agat.univ-lille1.fr, FR |
| |
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 linear friction force proportional to its velocity (at small speeds). The medium consists at each point in a 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.
Received: 18 July 2001 / Accepted: 20 April 2002 Published online: 12 August 2002 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|