Geodesic
Hamiltonians representing equations of motion with damping due to friction
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Suppose that $$ \dot q = \frac{\partial H}{\partial p}(q,p) , \quad \dot p = - \frac{\partial H}{\partial q}(q,p) - \frac{\partial \tilde L}{\partial \dot q}(q,\dot q) $$ The method is to embed M into a larger framework where the motion drives a wave equation on the negative half line, where the energy in the wave represents heat being carried away from the motion. We obtain a version of Nother's Theorem that is valid for dissipative systems. We also show that this framework fits the widely held view of how Hamiltonian dynamics can lead to the "arrow of time."
Classification : 70H25
Keywords: Hamiltonian, Lagrangian, Rayleigh dissipation function, friction, nother's theorem 
@article{EJDE_2014__2014__a100,
     author = {Montgomery-Smith, Stephen},
     title = {Hamiltonians representing equations of motion with damping due to friction},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a100/}
}
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Montgomery-Smith, Stephen. Hamiltonians representing equations of motion with damping due to friction. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a100/