Hamilton’s equation of motion in PB formulation | Poisson’s theorem | Classical mechanics

Hamilton’s equation of motion in Poisson Bracket formulation

Poisson’s theorem

• From Hamilton’s equation of motion

• If u is a constant of motion, then du/dt = 0

            

• If u does not explicitly depend on time, then ∂u/∂t = 0

            

• This is Poisson theorem in classical mechanics

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