- #1
blueberrypies
- 6
- 0
\underbrace{d}_{dt} (\dot{x})^{2} = 2\ddot{x} ? or is it just 2\dot{x} ?
Understanding the Derivative of Angular Velocity in Lagrangian Mechanics
- Context: Graduate
- Thread starter blueberrypies
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the derivative of angular velocity in the context of Lagrangian mechanics, specifically addressing the application of the chain rule and the interpretation of symbols in the Lagrangian formulation.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- One participant questions whether the derivative of the square of velocity should be expressed as \(2\ddot{x}\) or \(2\dot{x}\).
- Another participant suggests that neither option is correct and advises the use of the chain rule for clarification.
- A later post indicates a lack of understanding regarding a specific expression in the book, prompting a request for help.
- One participant clarifies that the derivative with respect to \(\theta'\) can be treated as a symbol that can be replaced by another variable, suggesting flexibility in notation.
- A subsequent response acknowledges this clarification with appreciation.
Areas of Agreement / Disagreement
The discussion contains multiple competing views regarding the correct interpretation of derivatives in Lagrangian mechanics, and it remains unresolved as participants express differing opinions and seek clarification.
Contextual Notes
Participants express uncertainty about specific mathematical expressions and their interpretations, highlighting potential limitations in understanding the application of the chain rule and notation in Lagrangian mechanics.
- #2
tiny-tim
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welcome to pf!
hi blueberrypies! welcome to pf!
neither
…
use the chain rule
hi blueberrypies! welcome to pf!
neither
…use the chain rule
- #3
blueberrypies
- 6
- 0
nevermind. I'm going to work on this more.
- #4
- #5
tiny-tim
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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 '
for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '
- #6
blueberrypies
- 6
- 0
tiny-tim said: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!
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