Definition:Lagrangian
Jump to navigation
Jump to search
Definition
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 $P$.
Source of Name
This entry was named for Joseph Louis Lagrange.
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |