is stationary for the functions y1(t), y2(t),…,yn(t), describing the development in time for the system.
that is, the difference between the kinetic energy T and the potential energy V.
is called the action integral.
Remark 2: Hamilton’s principle mean that among all curves between the end points, the motion will occur along the curve that gives an extreme value (actually stationary value) to the action integral.
In the special case when we are dealing with mechanical systems these equations are called Lagrange’s equations.