Definition:Action Applied by System

Definition
The action applied by a system from state $1$ to state $2$ is defined as the definite integral of the Lagrangian over time from state $1$ to state $2$.


 * $\displaystyle S_{12} = \int_{t_1}^{t_2} \mathcal L \ \mathrm{d}{t}$

where $S_{12}$ is the action from $1$ to $2$, $t$ is time, and $\mathcal L$ is the Lagrangian.