Definition:Generalized Momentum

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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:

$p_i = \dfrac {\partial \LL} {\partial \dot q_i}$

where:

$p_i$ is the $i$th coordinate of the generalized momenta
$\LL$ is the Lagrangian
$\dot q_i$ is the time derivative of the generalized coordinates $q_i$.


Sources