Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-01-30
Physics
Condensed Matter
Statistical Mechanics
9 pages
Scientific paper
The least action principle of mechanics is extended to damped system by considering the Lagrangian function of a total system which contains a damped moving body and its environment, both coupled by friction. Although the damped body is nonconservative system, the energy of the total system is conserved since energy is only transfered by friction from the body to the environment. Hence the total system can be considered as a Hamiltonian system whose macroscopic mechanical motion should a priori obey the least action principle. The essential of the formulation is to find a Lagrangian of the total system for the calculation of action. This is solved thanks to a potential like expression of the dissipated energy whose derivative with respect to the instantaneous position of the damped body yields the friction force. This Lagrangian was also derived from the virtual work principle which is not limited to Hamiltonian system. We think that this extension opens a possible way to study the relationship between two independent classes of variational principles, i.e., those of Hamiltonian/Lagrangian mechanics and those associated with energy dissipation. An application to quantum dissipation theory can be expected via the path integral formulation of quantum mechanics.
Wang Qiuping A.
Wang Ru
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