abstract:In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time-evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate-transformations, called canonical transformations, which maps canonical coordinate systems into canonical coordinate systems.
Based on the Poissonbracket and thediscriminant of integral of motion, we prove the problem that the moment ofmomentumis the integral of motion when the mass pointis affected by central force.