= Lagrangian vs Hamiltonian
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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:
* https://physics.stackexchange.com/questions/89035/whats-the-point-of-hamiltonian-mechanics
* https://www.quora.com/What-is-the-difference-between-a-Lagrangian-and-a-Hamiltonian