Euler-Lagrange Equation: Constraints and Multiple Dependent Variables

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...
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