A function of the generalized coordinates and velocities of a dynamical system from which the equations of motion in Lagrange's form can be derived. The Lagrangian function is denoted by L(q1, …, qf; ˙q1, …, ˙qf; t). For systems in which the forces are derivable from a potential energy V, if the kinetic energy is T, the equation below holds. See Lagrange's equations
(or kinetic potential), expressed in terms of generalized coordinates qi, generalized velocities coordinates gi, generalized velocities q̇i, and time t. In the simplest case of a conservative system, the Lagrangian function is equal to the difference between the kinetic energy T and the potential energy Π of the system expressed in terms of qi and qi, that is, L = T(qi, q̇i, t) —Π (q̇i). If we know the Lagrangian function, it is possible to construct differential equations of motion of a mechanical system using the principle of least action.