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Lagrangian Function

A Lagrangian function in the calculus of variations is a function L(q,q^.,t) that serves as the integrand of an action integral

S[q]=intL(q,q^.,t)dt.

Under suitable regularity and endpoint conditions, stationary curves of S satisfy the Euler-Lagrange differential equation

d/(dt)(partialL)/(partialq^._i)-(partialL)/(partialq_i)=0.

In mechanics, q denotes the coordinates of a system, q^. their velocities, and t time.

See also

Action Integral, Calculus of Variations, Euler-Lagrange Derivative, Euler-Lagrange Differential Equation

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References

Gelfand, I. M. and Fomin, S. V. Calculus of Variations. Mineola, New York: Dover, 2000.Goldstein, H. Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, 1980.

Cite this as:

Weisstein, Eric W. "Lagrangian Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LagrangianFunction.html

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