Ciro Santilli
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The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs:
  • generalized coordinates
  • their corresponding conjugate momenta
This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.
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Ancestors

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