When is Hamiltonian mechanics useful

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Hamiltonian mechanics is particularly useful for problems involving phase space flows, offering a more intuitive perspective compared to Lagrangian mechanics. Both formalisms are equivalent and based on the same principles, making the choice between them largely a matter of preference. For instance, Roger Penrose prefers the Hamiltonian approach for its perceived symmetry. Understanding Hamiltonian mechanics can also facilitate a smoother transition into quantum mechanics. Ultimately, the discussion highlights the subjective nature of choosing between Hamiltonian and Lagrangian methods.
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Generally, what sort of problems are handled better by Hamiltonian mechanics than by Lagrangian mechanics? Can anyone give a specific example?
 
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Your first exposure to quantum mechanics will be made easier with a working knowledge of Hamiltonian Mechanics.

Really they just provide a different way of looking at a problem, mainly through the more intuative phase space flows. Hamiltons and Lagranges equations are completely equivelant.
 
Given that the lagrangian and Hamiltonian formalisms are exactly equivalent and based on the same principles, it's more a question of taste. For example, Roger Penrose says he finds the Hamiltonian approach to be more "symmetric".
Come on, those poisson brackets are tasty :p
 

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