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
 * $\mathcal L$ is the Lagrangian.