Jacobi integral in CR3BP via canonical Poisson bracket: {x, H} = dH/dp_x = Omega y + p_x

Jacobi-integral framework via canonical Poisson brackets (Jacobi 1836). Setup: in the circular restricted three-body problem (CR3BP), the Hamiltonian in the rotating frame is H = (p_x^2 + p_y^2)/2 + Omega^2 (x^2 + y^2)/2 - Omega (x p_y - y…