Definition:Generalized Momentum

Definition
The generalized momentum of analytical (Lagrangian, Hamiltonian) formulations of classical mechanics is defined as the partial derivative of the Lagrangian with regards to the time derivative of generalized coordinates:


 * $ p_i = \dfrac{\partial\mathcal L}{\partial \dot{q}_i}$

where $p_i$ is the ith coordinate of the generalized momenta, $\mathcal L$ is the Lagrangian, and $\dot{q}_i$ is the time derivative of the generalized coordinates $q_i$.