On the Dirac Approach to Constrained Dissipative Dynamics

Details On the Dirac Approach to Constrained Dissipative Dynamics On the Dirac Approach to Constrained Dissipative Dynamics

2001-10-23

arxiv.org/abs/physics/0110065v1

Journal of Physics A: Math. Gen. 34, No. 43, 9281-9302, 2001

Physics

Classical Physics

22 pages, LaTeX document, pedagogical presentation

Scientific paper

10.1088/0305-4470/34/43/312

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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