On the Dirac Approach to Constrained Dissipative Dynamics
Sonnet Q H Nguyen, Lukasz A Turski
Abstract
In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for constrained dissipative systems through an extension of the Dirac brackets concept, and we present a new formula for calculating Dirac brackets. This formula is particularly useful in the description of dynamical systems with many second-class constraints. After presenting the necessary formal background we illustrate our method on several examples taken from particle dynamics, continuum media physics and wave mechanics.
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