Equations of Motion for the Double Pendulum (2DOF) Using Lagrange's Equations

Deriving the equations of motion for the double pendulum using the method of Lagrange's equations. Two degree of freedom system.

[spencergee]

It's encouraging to note that if, in equation 19, m2 and l2 are equal to zero, the equation reduces to that of the simple pendulum.

The soundtrack played at 8:27 almost gave me a heart attack.

[eleanorterry-welsh]

You are single handedly saving my butt in this mechanics course I'm in. I have had a hard time understanding the text book we're using, but you usually have a video on whatever the topic of the week is, and watching your explanations first and then going to class/reading the textbook has been a much better way for me to figure out what is going on than just ineffectually staring at my textbook and feeling stupid.

[ontheline]

You have literarly saved me, dude. Thanks.

[jensknudsen]

My computer doesn't even have a font as neat as your hand writing.

[pratibhasingh]

Omg. You are just wonderful. I really had hard time understanding this concept. but you broke down it into simpler steps that are easy to follow. Thanks a lot for helping out. God bless you.

[kitsukeita]

Double pendulum coding solutions? Thanks for saving me a ton of time in case my teacher asks to 'explain the formulae'. Love from India.

[gtweak]

Your channel is my discovery of this year. Thank you for your work.

[Listener]

There's a random YouTube video of a Japanese guy demonstrating a double pendulum. Watched it, and kept on clicking the related videos until I get here. Funny the equations made sense somehow. I was lost on partial derivation. Anyways, great video.

[ashutoshsharma]

Very good explanation in a very lucid manner.... Thanks a lot for the video....

[emmyobasi]

Thanks a lot. Your teaching style is amazing.

[ShadowWalker]

Hi, great video, helped me a lot. Just one question, in the last equation found (23), wouldn't it be possible to take m2 off every term?

[akhilvarghese]

Such a great video thank you so much, very comprehensive!

[gotango]

Thanks for the video and explanation. Helped a lot.

[hostkakamay]

it's fine until now but how to find the natural frequency for this system of pendulum?

[mahirahmed-al]

Hi, I was going through some of the algebra while trying to do this problem myself with the help of your video and I think you may have made an error in 19:33 where you find the partial of the lagrange with respect to partial theta 2. I think you missed a negative symbol when finding the derivative of cos(theta1 - theta2). Great video, though, thanks for it. Helped a bunch!

[lokmanhossainlokman]

It literally scared me at 8:29 ngl.
However, great video <3

[Akash-tlrm]

Can you please explain through equations of motion, how double pendulum is an example of chaotic system.

[mathieulebrun]

at the 9:49 mark... where does the 3rd term for the KE come from? The one simplified by the the double angle identity provided at the beginning. By my understanding factoring out the the l1, thea1 & l2, theta2 terms should yield 2 terms that simplify to 1... (sin^2 + cos^2) =1, where does the 3rd term come from?

[alexroumanidakis]

Right around the 18:12 mark it appears you forgot the (theta dot 1 - theta dot 2) term from the time derivative component, you missed it on both equations of motion actually. Is there some unmentioned reason that term goes away?