# Lagrangian Function

## Lagrangian function

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*(*q*_{1}, …, *q** _{f}*;

*˙q*

_{1}, …,

*˙q*

*;*

_{f}*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

## Lagrangian Function

(or kinetic potential), expressed in terms of generalized coordinates *q _{i},* generalized velocities coordinates

*g*generalized velocities

_{i},*q̇*and time t. In the simplest case of a conservative system, the Lagrangian function is equal to the difference between the kinetic energy

_{i},*T*and the potential energy Π of the system expressed in terms of

*q*and q

_{i}*that is,*

_{i},*L = T(q*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.

_{i}, q̇_{i}, t) —Π (q̇i).