Definition:Action Applied by System

This page is about action applied by a system. For other uses, see action.

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 $2$:

$\ds S_{12} = \int_{t_1}^{t_2} \LL \rd t$

where:

$S_{12}$ is the action from $1$ to $2$

$t$ is time

$\LL$ is the Lagrangian.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): action: 2. (Mechanics)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): action (in dynamics)