Finding the angular momentum along an axis given the Lagrangian and equation of motion

  • #1

Homework Statement:

Finding the angular momentum along an axis given the eqs of motion

Relevant Equations:

$${\ddot{z} = \frac{g}{1+(\frac{4R}{s})^2}}$$
with s being the distance along z axis after a revolution
given z(0) = 0 as well as

˙z(0)=0​

How would one find the angular momentum along the x axis in terms of t.
Currently, I have formulated the following:


$${\ddot{z} = \frac{g}{1+(\frac{4R}{s})^2}}$$
 
Last edited:

Answers and Replies

  • #2
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Seems like this is part of a more complete problem. State that.
Currently, I have formulated the following:
$$\ddot{z} = \frac{g}{1+(\frac{2\pi R}{k})^2}$$
Currently you have ##z(t)=0##.

And a { too many in your ##\TeX## :wink:
 
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  • #3
Seems like this is part of a more complete problem. State that.

Currently you have ##z(t)=0##.

And a { too many in your ##\TeX## :wink:
Thanks for clearing that up I was trying to understand the Latex code -
 
  • #4
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Currently you have z(t)=0z(t)=0. [edit] no, ##a\,t^2##

And enclose ##\LaTeX## in double $$ or (## for in-line )
 
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  • #5
Thanks for the help I hope it is now readable.
My question is how do I formulate the angular momentum from the world of the x axis as a function of time.
 
  • #6
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Maybe you missed this:
Seems like this is part of a more complete problem. State that.
It means: please provide a complete problem statement.

From the PF guidelines:
micromass said:
Reproduce the problem statement accurately.
Type the problem statement exactly as worded. If you're only asking about one part of a long problem it may not be necessary to type up the entire problem, but you need to ensure you've provided the proper context for the sub-problem. If you paraphrase or summarize, make sure you're not changing the meaning or omitting important information. It's very frustrating trying to help with a problem only to discover that critical information is missing.
No idea why you have a picture with x,y,z, formulas with z only.
No idea about R, s (k?, ##\lambda##?),

My question is how do I formulate the angular momentum from the world of the x axis as a function of time
I don't think the world of the x-axis has angular momentum. Usually ##\vec L = \vec r \times \vec p## :wink: .
 
  • #7
Maybe you missed this:

It means: please provide a complete problem statement.

From the PF guidelines:

No idea why you have a picture with x,y,z, formulas with z only.
No idea about R, s (k?, ##\lambda##?),


I don't think the world of the x-axis has angular momentum. Usually ##\vec L = \vec r \times \vec p## :wink: .
Yep sorry I was trying to understand an issue rather than a paper problem. It was an error in my thinking I realize now. Please feel free to remove this q I don't seem able to.
 

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