Conjugate momenta - Aetherwisp

Conjugate momenta are dynamical variables that generalize the idea of momentum to generalized coordinates in both Lagrangian and Hamiltonian systems.

Given a Lagrangian $L$ with $n$ degrees of freedom over the generalized coordinate $q(t)$ , the $l$ -th conjugate momentum is defined as

P_{l}(q,\dot{q},t)\equiv \frac{ \partial L }{ \partial \dot{q}_{l} } (q,\dot{q},t)