Principle of Least Action

It must be called stationary-action principle.
The function $α$ describing a system is the result of a variational problem, the optimization (maximum or minimum) of the functional action given by

S (α, t_{1}, t_{2}) := \int_{t_{1}}^{t_{2}} L (α (t), \dot{α} (t), t) d t

where $L$ is a function specific for the studied system called the Lagrangian of the system. This "stationary path" can be obtained with the Euler-Lagrange equations.

Additionally, there is an action for Hamiltonian mechanics.