Generalized coordinates and constraints in Lagrangian mechanics

Рет қаралды 12,643

3 жыл бұрын

Classical Mechanics and Relativity: Lecture 7
Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete and self-contained course in which everything is derived from scratch.
In this lecture I discuss degrees of freedom and generalized coordinates in classical mechanics, configuration / state space vs phase space, and constraints. In particular, we will look at how constraints can be implemented automatically through a careful choice of generalized coordinates within the Lagrangian framework -- provided the constraints are holonomic. We will look at examples of non-holonomic systems, which are yield counter-intuitive and surprising physical results.
Full lecture course playlist: • Classical Mechanics an...
Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler

Пікірлер: 16

@VIVI-fi4jy 3 жыл бұрын

Your series is hands down the best I've found, my class structure avoids introducing the hamiltonian and the principle of least action until lagrangian is fully covered but the way you introduced everything is way more intuitive and your explanations are so neat, haven't struggled much with the class thank to your videos

@mehdisaissi 5 ай бұрын

A heartfelt thank you from moroco

@deepblueftw 3 жыл бұрын

Wow..Thank u very much.. I hope ur channel blows up soon cause the content deserves more views.. Plz keep apploading such videos.. They help me nail my college tests.

@2000ustham 2 ай бұрын

Brilliant stuff thumbs up

@josue7576 2 жыл бұрын

Great lecture! Thank you so much.

@2000ustham 6 ай бұрын

Brilliant stuff ,you just made it look so simple

@tjerkvanderweij9622 Жыл бұрын

very informative video thanks!

@_shaka_ 2 жыл бұрын

superb

@dragonball4333 3 жыл бұрын

Good job

@user-fw6fo4wx3f Жыл бұрын

Hi Dr Mitchell! I recently discovered your channel and your lectures are exceptional!! I wonder if you could make available the notes you wrote in the lectures as a pdf?

@nishmabhattarai9743 2 жыл бұрын

This video is the best explanation for generalized coordinates and constraints.Thank you very much. Can you recommend some books which explains clearly as you have explained in this video?

@drmitchellsphysicschannel2955 2 жыл бұрын

Thanks for the question! Yes, I really like Morin's classic Classical Mechanics textbook for this material.

@louis4798 2 жыл бұрын

looking forward to the General Relativity Playlist!!!

@lambda2693 Жыл бұрын

nice photo man

@louis4798 Жыл бұрын

@@lambda2693 indeed

@saharsoumeeh9341 2 жыл бұрын

thanks a lot for sharing these amazing lectures. I have a question about the way of writing lagrangian for spin dynamics and calculating equation of motion for antiferromagnets and skyrmions. I will be grateful if you could kindly reply to my question or could introduce me a good source to study.