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For a given conservative dynamical system, the Lagrangian is L=T-V, where T is the kinetic energy of the system and V is its potential energy. L is a function of the generalised coordinates q_i and generalised velocities [(q)\dot]_i of the system.
It can be shown that the equations of motion for a conservative system in this case are [(d)/(dt)] ( [(∂L)/(∂[(q)\dot]_j)] ) − [(∂L)/(∂q_j)] = 0 .
An analogous function can be defined, giving a similar equation of motion, for a non-conservative system.