The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs:
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.
- generalized coordinates
- their corresponding conjugate momenta
- Hamiltonian mechanics | 78, 215, 3