Uploaded March 2018 | Updated September 2026, 2 weeks ago
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. youtube.com/watch?v=6HeQc7CSkZs&index=1&list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_&t=0s
2. youtube.com/watch?v=sFqp2lCEvwM&list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_&index=2
Lecture Notes: drive.google.com/open?id=1i4vmv1ElkHX9jXaWDcKhHhI9ppGu8NBP
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/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
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. youtube.com/watch?v=6HeQc7CSkZs&index=1&list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_&t=0s
2. youtube.com/watch?v=sFqp2lCEvwM&list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_&index=2
Lecture Notes: drive.google.com/open?id=1i4vmv1ElkHX9jXaWDcKhHhI9ppGu8NBP
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/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
