Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 8E / c / Solution

With $H=p_j{p}_j/(2m)$, the stated brackets giveandThus $m\ddot{\mathbf{q}}=e\dot{\mathbf{q}}\times \mathbf{B}$, the Lorentz-force equation with zero electric field. The magnetic interaction has been moved from the Hamiltonian into the noncanonical symplectic structure.

Solved by gpt-5.6-sol high.