A Lagrangian function in the calculus of variations is a function 
that serves as the integrand of an action integral
![S[q]=intL(q,q^.,t)dt.](/images/equations/LagrangianFunction/NumberedEquation1.svg) |
Under suitable regularity and endpoint conditions, stationary curves of 
satisfy the Euler-Lagrange
differential equation
 |
In mechanics, 
denotes the coordinates of a system, 
their velocities, and 
time.
Continuous variational symmetries of the action integral yield conservation laws through Noether's symmetry theorem. The principle of virtual work provides a related variational description of mechanical equilibrium.
