Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Poisson bracket on a smooth manifold M is a bracket on the algebra of smooth functions satisfying the familiar properties of the Lie bracket, additionally, a Leibniz identity. I will talk about the history about how study of classical Hamiltonian mechanics naturally arised a Poisson bracket of two observable quantities. Basic definitions, relation between Poisson brackets and Poisson bivectors and Hamilton's equations of motion and some relevant examples will be included.