Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 8B / a / Solution

The Jacobi identity for the Poisson bracket isFor quantities with no explicit time dependence,If $F$ and $G$ are conserved, the first two terms of the Jacobi identity vanish. Henceor, by antisymmetry,Thus the poisson bracket of conserved quantities is itself conserved.