A true least action principle for damped motion

Qiuping A. Wang (1, 2) , Ru Wang

1 IMMM - Institut des Molécules et Matériaux du Mans
2 ESIEA - Ecole Supérieure d'Informatique Electronique Automatique [Paris]

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Mécanique [physics]; Physique Quantique [quant-ph]

Qiuping A. Wang, Ru Wang. A true least action principle for damped motion. Journal of Physics: Conference Series, 2018, 1113, pp.012003. ⟨10.1088/1742-6596/1113/1/012003⟩. ⟨hal-02146637⟩