Variational Calculus. Functional. Calculus operates on functions of one or more variables. Example: derivative to find a minimum or maximum Some problems involve a functional. The function of a function Example: work defined on a path; path is a function in space. Path Variation.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
for all h(x)
Fixed at boundaries
h(x1) =h(x2) = 0Boundary Conditions
The quantity in brackets must vanish.
This is Euler’s equation.
General mathematical relationshipEuler’s Equation
Action is a functional
Extends to multiple coordinates
The Euler-Lagrange equations are equivalent to finding the least time for the action.
Multiple coordinates give multiple equations
This is Hamilton’s principle.Action