[LECS/CM-04003]

We define Poisson bracket and the Hamiltonian equations of motion are written in terms of Poisson brackets. The equation for time evolution of a dynamical variable is written in terms of Poisson brackets. It is proved that a dynamical variable \(F\), not having explicit time dependence, is constant of motion if its Poisson bracket with the Hamiltonian is zero.

We list important properties of Poisson brackets. Poisson bracket theoerem statement that the Poisson bracket of two integrals of motion is again an integral of motion, and its proof is given. A generalization of the theorem is given without proof.