Asymmetric Free Top: Euler's Equations & Stability

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Homework Help Overview

The discussion revolves around the dynamics of an asymmetric free top, specifically focusing on Euler's equations and the stability of motion under perturbations. The original poster presents a series of questions regarding the conditions for equilibrium and the effects of small perturbations on the system's motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the conditions under which certain angular velocities are solutions to Euler's equations. There is a focus on understanding the implications of small perturbations and the resulting linear equations. Some participants express confusion about the problem and seek clarification on how to approach it.

Discussion Status

There is an ongoing exploration of the problem, with participants questioning the original poster's understanding and suggesting the need to clarify key concepts such as Euler's equations. Some expressions of uncertainty indicate a lack of consensus on how to proceed, while others are attempting to guide the discussion towards a more structured approach.

Contextual Notes

Participants note the original poster's feelings of being overwhelmed and the need for clearer guidance on the problem's requirements. There are hints of imposed homework rules regarding the format of responses, which may affect how participants engage with the problem.

Shafikae
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Consider the asymmetric free top with I1 [tex]\neq[/tex] I2 [tex]\neq[/tex] I3

1) Show that [tex]\omega[/tex]1 = [tex]\Omega[/tex] = const. and
[tex]\omega[/tex]2 = [tex]\omega[/tex]3 = 0 is a solution to Eulers equations.

2) Consider a small perturbation about the spin of the form
[tex]\omega[/tex]1 = [tex]\Omega[/tex] + v1
[tex]\omega[/tex]2 = v2
[tex]\omega[/tex]3 = v3
and assume that the vk are small. What is the system of linear equations for the vk?

3) Find the general solution to the system of equations and interprete the result in terms of stability of the motion.
 
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You stated your homework problem clearly. So what is your question?
 
I don't understand any of it! I don't know what to do, I don't know how to begin solving it. I'm a helpless case :(
 
Shafikae said:
I don't understand any of it! I don't know what to do, I don't know how to begin solving it. I'm a helpless case :(
Use the template for homework posts:

Homework Statement



Homework Equations



The Attempt at a Solution


It would lead you to the first thing I'd suggest here...
Namely since the the problem refers to Euler's Equations, why don't you post those to show us you know what they are.
 
Schaefer would be displeased!
 
I got it thank you!
 

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