\begin{definition}[Definition:Lagrangian]
Let $P$ be a physical system composed of $n \in \N$ particles.
Let the real variable $t$ be the time of $P$.
$\forall i \le n$ let $\map { {\mathbf x}_i} t$ be the position of the $i$th particle.
Suppose, 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 $P$.
{{NamedforDef|Joseph Louis Lagrange|cat = Lagrange}}
Category:Definitions/Lagrangian Mechanics
Category:Definitions/Physics
Category:Definitions/Applied Mathematics
\end{definition}