Principle of stationary action

The principle of stationary action for the Action (physics) S (a measure of the energy of the system under study) states that the variation in S is at an extremum, in symbols:

where the independent variables are denoted by a set of x_i(t) acting at some time t.

See: Action (physics) #Euler-Lagrange equations for the action integral for the conditions when this principle is true.

Extremum can in fact mean a local minimum, a local maximum, or a stationary value.