Hamilton's equations are $\dot x_i=p_i$ and $\dot p_i=-\partial_iV$. A first <integral> $F$ satisfies $\{F,H\}=0$. See <integrable Hamiltonian system>: in three degrees of freedom, integrability requires three independent commuting first <integrals>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 33B / a / Solution

 Solution (source code)