Séminaire de groupe
|Théorème de Noether et constantes du mouvement en présence de frottements visqueux|
|Equipe 106, Institut Jean Lamour|
|jeudi 19 juin 2014 , 10h25|
|Salle de séminaire du groupe de Physique Statistique|
Starting from a lagrangian description of a moving particle under the effect of a static potential and a dissipative force proportional to its velocity, we infer the constants of motion that can be deduced from the Noether’s theorem by using spatio-temporal point transformations. This is firstly achieved for the one dimensional case where only a few generic potentials are concerned. The case of radial potentials is essentially similar the one dimensional case, except that the rotational invariance results in the exponential decrease of the angular momentum over time. All the constants we found are explicitly time-dependent. Some of these are energy-like in the sense that they tend toward the energy of the associated conservative problem when the dissipative parameter tends toward zero. A canonical transformation is then constructed in the extended phase space of the problem in order that these constants become a time-independent Hamiltonian when expressed as a function of the new variables. Finally, we discuss the existence of an “energy-like” theorem for these dissipative systems.