1201.6309 (Qiuping A. Wang et al.)

Is it possible to formulate least action principle for dissipative
system?    [PDF]

Qiuping A. Wang, Ru Wang

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.

View original: http://arxiv.org/abs/1201.6309