Let a two-degree-of-freedom system be described by the Hamiltonian1H =(P +P)+ V(x, y)and suppose the potential energy V is a homogenous function of degree -2:V(xx, ày) = 2-2v(x,y) VÀ > 0.Show that$ = (xpy – yp.)² +2(x² + y²)V(x, y)is a second constant of the motion independent of the Hamiltonian (Yoshida, 1987).Therefore, this system is integrable.

Given Hamilton : And the potential energy V is a homogeneous function of degree -2 for all

Let a two-degree-of-freedom system be described by the Hamiltonian = 1/ (p² + p ²) + V(x, y) and suppose the potential energy V is a homogenous function of degree -2: V(λx, y) = λ-2V(x, y) > Show that Þ= (xpy - ypx)² + 2(x² + y²)V(x, y) is a second constant of the motion independent of the Hamiltonian (Yoshida, 1987). Therefore, this system is integrable.

Let a two-degree-of-freedom system be described by the Hamiltonian = 1/ (p² + p ²) + V(x, y) and suppose the potential energy V is a homogenous function of degree -2: V(λx, y) = λ-2V(x, y) > Show that Þ= (xpy - ypx)² + 2(x² + y²)V(x, y) is a second constant of the motion independent of the Hamiltonian (Yoshida, 1987). Therefore, this system is integrable.