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by Ciro Santilli (@cirosantilli, 37)

Lagrangian vs Hamiltonian

 ... Science Natural science Physics Mechanics Lagrangian mechanics Hamiltonian mechanics
 0 By others on same topic  0 Discussions  Updated 2025-05-29  +Created 1970-01-01  See my version
The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:
  • generalized coordinates, generally positions or angles
  • their corresponding conjugate momenta, generally velocities, or angular velocities
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.
Bibliography:
  • physics.stackexchange.com/questions/89035/whats-the-point-of-hamiltonian-mechanics
  • www.quora.com/What-is-the-difference-between-a-Lagrangian-and-a-Hamiltonian

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