Lagrange's equations are fundamental relations in Lagrangian mechanics given by

(1)

where is a generalized coordinate, is the generalized work, and T is the kinetic energy. This leads to

(2)

where L is the Lagrangian, which is called the Euler-Lagrange differential equation. Lagrange's equations can also be expressed in Nielsen's form.

Lagrangian, Lagrangian Mechanics, Nielsen's Form