Toronto Math Forum

APM346--2019 => APM346--Lectures & Home Assignments => Topic started by: Rhamel on April 09, 2019, 05:30:05 PM

Title: Exam Practice: Prob 69-72
Post by: Rhamel on April 09, 2019, 05:30:05 PM
When we are asked to "find the Euler-Lagrange of [some functional T[v]]" are we supposed to :
a) differentiate T[v+$\epsilon$ w] w.r.t to w and evaluate at $\epsilon = 0$ to get the EL, or
b) just plug the Lagrangian into

$$\frac{\partial}{\partial x_j} \frac{\partial \mathcal{L}}{\partial v_{x_j}} =  \frac{\partial \mathcal{L}}{\partial v}$$
Title: Re: Exam Practice: Prob 69-72
Post by: Victor Ivrii on April 09, 2019, 08:08:35 PM
You understand, that in the left there is summation with respect to $j$?
Title: Re: Exam Practice: Prob 69-72
Post by: Rhamel on April 09, 2019, 10:09:58 PM
yes