What does $\delta L(x,x')$ mean in variation calculus and Lagrangian mechanics? How is it different from the derivative? What does it mean to take $\delta$ of an action?
2026-03-26 06:09:31.1774505371
What does $\delta L$ mean in variation calculus?
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It's called the Gateaux Variation or Gateaux Derivative. It's a higher-level analogue of the derivative, but you are "taking the derivative" of a functional instead of a function. There are theorems in the Calculus of Variations that show you get extremals of $L$ when $\delta L=0,$ at least in many cases.