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: In physics, the action principle is an assertion about the nature of motion from which the trajectory of an object subject to forces can be determined. ... Energy is a fundamental quantity that every physical system possesses; it allows us to predict how much work the system could be made to do, or how much heat it can exchange. ... A variational principle is a principle in physics which is expressed in terms of the calculus of variations. ...

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. In physics, the action principle is an assertion about the nature of motion from which the trajectory of an object subject to forces can be determined. ...

Extremum can in fact mean a local minimum, a local maximum, or a stationary value. A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some ε > 0 such that f(x*) ≥ f(x) for all x with |x-x*| < ε. ... A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some ε > 0 such that f(x*) ≥ f(x) for all x with |x-x*| < ε. ...