Taylor expansion gives $δH=H_q\mathbin\cdotδq+H_p\mathbin\cdotδp=-ε\{F,H\}$. Hamilton's equation gives $\dot F=\{F,H\}$, so $F$ is conserved exactly when the generated infinitesimal canonical transformation leaves $H$ invariant.


Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 15D / c / Solution

 Solution (source code)