Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Functional Derivatives/Euler-Lagrange
Reply to thread
Message
[QUOTE="lippyka, post: 6891017, member: 602549"] Homework Equations The equation defining T is given in the statement. The Euler-Lagrange equation is as follows: \frac{\partial{f}}{\partial{x}} = \frac{d}{d \lambda} (\left \frac{\partial{f}}{\frac{d}{d \lambda}(\frac{\partial{f}}{\partial{x}})} \right) = 0 The Attempt at a SolutionTo solve this problem, you will need to use the Euler-Lagrange equation to take functional derivatives of T with respect to each function defining it. This can be done by taking the partial derivative of T with respect to each of these functions and then setting them to equal zero. For example, for s(\lambda), the partial derivative would be: \frac{\partial{T}}{\partial{s(\lambda)}} = \int_{\lambda_{1}}^{\lambda_{2}} \left (\frac{d}{d \lambda}(\sum_{j=1}^{d} s(\lambda) R_{j}^{i}(\lambda)(q_{I}^{j}(\lambda) + a^{j}(\lambda))) \right )^2 d\lambdaSetting this equal to zero, we get: \frac{d}{d \lambda}(\sum_{j=1}^{d} s(\lambda) R_{j}^{i}(\lambda)(q_{I}^{j}(\lambda) + a^{j}(\lambda))) = 0 Similarly, you can take the partial derivative of T with respect to each of the other functions defining it, and then set each one equal to zero. This will give you a system of equations that can be solved to find the conditions for which all of the functional derivatives are zero. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Functional Derivatives/Euler-Lagrange
Back
Top