Category:Lagrangians
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This category contains results about Lagrangians.
Definitions specific to this category can be found in Definitions/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 $P$.