Lagrangian mechanics-momentum&force

Lagrangian $L$.

Canonical momentum conjugate to $q_i$

$p_i={\partial L \over \partial \dot{q_i}}\tag{1}$

Generalized force conjugate to $q_i$

$F_i={\partial L \over \partial q_i}\tag{2}$

Lagrange’s Equation

${\partial L \over \partial q_i} -{d \over dt}\left( {\partial L \over \partial \dot{q_i}} \right) = 0\tag{3}$

From Principles of Quantum Mechanics, 2nd Edition by R. Shankar.

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Lagrangian for classical mechanics

$L=T-V$

, where $T$ = Kinetic Energy, $V$ = Potential Energy.