A true least action principle for damped motion
Abstract
This work is a formulation of the least action principle for classical mechanical dissipative systems. We consider a whole conservative system composed of a damped moving body and its environment receiving the dissipated energy. This composite system has a conservative Hamiltonian H = K1 + V1 + H2 where K1 is the kinetic energy of the moving body, V1 its potential energy and H2 the energy of the environment. The Lagrangian is found to be L = K1 − V1 − E d where E d is the energy dissipated from the moving body into the environment. The usual variation calculus of least action leads to the correct equation of the damped motion.
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