Category:Definitions/Lagrangians

This category contains definitions related to Lagrangians.
Related results can be found in Category:Lagrangians.

Let $P$ be a physical system composed of $n \in \N$ particles.

Let the real variable $t$ be the time of $P$.

For all $i \le n$, let $\map { {\mathbf x}_i} t$ be the position of the $i$th particle.

Suppose that the action $S$ of $P$ is of the following form:

$\ds S = \int_{t_1}^{t_2} L \rd t$

where $L$ is a mapping of (possibly) $t$, $\map { {\mathbf x}_i} t$ and their derivatives.

Then $L$ is the Lagrangian of $P$.