Theorem: Poisson bracket {x, H_CR3BP} = Omega y + p_x (Coriolis-shifted generalised velocity)

Theorem (CR3BP Poisson-bracket canonical): for the rotating-frame Hamiltonian H = (p_x^2 + p_y^2)/2 + Omega^2 (x^2 + y^2)/2 - Omega (x p_y - y p_x), the Poisson bracket {x, H} = dH/dp_x evaluates exactly to Omega * y + p_x. Canonical sympy…