  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.
