Lagrangian

The Lagrangian L of a system is simply the kinetic energy minus the potential energy:

L = T - V

This might seem like an uninteresting quantity, but it is the basis of much of classical mechanics. The Euler-Lagrange equation is

∂L/ ∂q = d/dt (∂ L/∂ q′ )

where q is known as a generalized position variable (such as the Cartesian coordinate x) and q′ is its time derivative. It is left as an exercise to the reader to show that this is equivalent to [Newton's Laws of Motion]?.