Suppose that is a Hamiltonian on a manifold M, and , the Rayleigh dissipation function, satisfies the same hypotheses as a Lagrangian on the manifold M. We provide a Hamiltonian framework that gives the equation
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.''
Submitted January 23, 2014. Published April 2, 2014.
Math Subject Classifications: 70H25.
Key Words: Hamiltonian; Lagrangian; Rayleigh dissipation function; friction; Nother's Theorem.
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| Stephen Montgomery-Smith |
Department of Mathematics, University of Missouri
Columbia, MO 65211, USA
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