Action

For a system described by the Lagrangian $L(\mathbf{q},\mathbf{\dot{q}},t)$ , the action (over the interval $t ε[t 1, t 2]$ ) is defined as

$S = \int_{t_1}^{t_2}{L(\mathbf{q},\mathbf{\dot{q}},t) dt}$