On the Dirac Approach to Constrained Dissipative Dynamics

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.

22 pages, LaTeX document, pedagogical presentation

References in corpus (3)

• Weak Dirac bracket construction and the superparticle covariant quantization problem
• Canonical description of incompressible fluid -- Dirac brackets approach
• Dirac Quantization of the Chern-Simons Field Theory in the Coulomb Gauge

Cited by in corpus (3)

• Recursive properties of Dirac and Metriplectic Dirac brackets with Applications
• Nambu mechanics for stochastic magnetization dynamics
• Leibniz-Dirac structures and nonconservative systems with constraints