Past exam of the theoretical physics I course of the University of Cambridge / 2015 / Paper 1 / 3 / a / Solution

For canonical coordinates $(q_i,p_i)$, the Poisson bracket isIt is bilinear and antisymmetric, obeys the Leibniz rule in either argument, and satisfies the Jacobi identity. These properties encode the symplectic structure of phase space. The two printed inline applications are treated separately below.