Question

Proof poisson bracket of any two constants of motion is a constant of motion

Answer 1

Prove that the Poisson bracket of two constants of the motion is itself a constant of the motion even when the constants depend upon time explicitly. ... Show by direct computation that the partial derivative of F with t, which is a constant of the motion, agrees with [H, F].

Answer 2

Prove that the Poisson bracket oftwo constants of the motion is itself aconstant of the motion even when the constants depend upon time explicitly.