On the lagrangian description of dissipative systems

Abstract

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and conserved quantities like the Hamiltonian, that generate symmetry transformations and do not correspond to observables. We show that there are simple relations among the equations satisfied by these two types of quantities. In the case of the damped harmonic oscillator, from the quantities obtained by Noether theorem follows the algebra of Feshbach and Tikochinsky. Further, if we consider the whole dynamics, the degrees of freedom separate into a physical and an unphysical sector. We analyze several cases, with linear and nonlinear dissipative forces; the physical consistency of the solutions is ensured observing that the unphysical sector has always the trivial solution.

14 pages

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• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
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• Higher-order contact mechanics
• Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography
• On the analytic representation of Newtonian systems
• Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow
• Quantization of nonlinear non-Hamiltonian systems
• Constrained Lagrangian dissipative contact dynamics