Principle of Least Action

Physical Law

The Principle of Least Action is a physical law which states the following:

Let $S$ be a dynamical system moving under conservative forces from point $A$ to point $B$.

The motion of $S$ takes place in such a way that the action has a stationary value with respect to all other possible trajectories from $A$ to $B$ with the same kinetic plus potential energy.

Proof

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Historical Note

The Principle of Least Action was first put forward by Pierre Louis Moreau de Maupertuis in $1744$, and since modified.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): least action, principle of
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): least action, principle of