Youtor
EulerLagrange Equation Constraints and Multiple Dependent Variables
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=pdO14dqC_nI
In this video, I begin by deriving the Euler-Lagrange Equation for multiple dependent variables. I show that in order to make a functional involving multiple y's stationary, it is necessary to solve an Euler-Lagrange equation for each of those y's. This is going to be useful when we work in 2-D or 3-D coordinate systems to solve Action Problems in Classical Mechanics. • In the second part of the video, I show how to approach variational problems when there are one or more constraints involved. The technique described comes from Lagrange multipliers and is a relatively simple one. This will also come in handy for my classical mechanics videos where there are constraints imposed on the particle's motion. • Questions/requests? Let me know in the comments! • Prereqs: Just these two videos (you could probably watch the rest of the playlist too, which is what I would recommend): • 1. • Introduction to Calculus of Variations • 2. • Derivation of the Euler-Lagrange Equa... • Lecture Notes: https://drive.google.com/open?id=1i4v... • Patreon: https://www.patreon.com/user?u=4354534 • Twitter: / facultyofkhan • Special thanks to my Patrons for supporting me at the $5 level or higher: • Jose Lockhart • Yuan Gao • Justin Hill • Marcin Maciejewski • Jacob Soares • Yenyo Pal • Chi • Lisa Bouchard
#############################
