Understanding the Derivative of Angular Velocity in Lagrangian Mechanics

[blueberrypies]

\underbrace{d}_{dt} (\dot{x})^{2} = 2\ddot{x} ? or is it just 2\dot{x} ?

 

[tiny-tim]

welcome to pf!

hi blueberrypies! welcome to pf!

neither …

use the chain rule

 

[blueberrypies]

nevermind. I'm going to work on this more.

 

[blueberrypies]

Alright, I still haven't figured this out so if anyone can help point out what I'm missing I would greatly appreciate it.

My book has this

But I don't get this. Shouldn't it be

 

[tiny-tim]

no, that would be ∂L/∂t

for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '

 

[blueberrypies]

no, that would be ∂L/∂t

for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '

Ohhh!

I see what you are saying :) Thanks!