Question

Discuss stationary values of a definite integral in classical mechanics

Answer 1

In other words, the action satisfies a variational principle: the principle of stationary action (see also below). The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral.

Answer 2

action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result.