Poisson bracket

The Poisson bracket is a mathematical operator used in classical mechanics, particularly in the context of Hamiltonian mechanics. It provides a way to describe the time evolution of dynamical systems and facilitates the formulation of Hamilton's equations of motion. The Poisson bracket is defined for two functions \( f \) and \( g \) that depend on the phase space variables (typically positions \( q_i \) and momenta \( p_i \)).