Asymmetric Free Top: Euler's Equations & Stability

[Shafikae]

Consider the asymmetric free top with I₁ $$\neq$$ I₂ $$\neq$$ I₃

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

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

3) Find the general solution to the system of equations and interprete the result in terms of stability of the motion.

 

[jambaugh]

You stated your homework problem clearly. So what is your question?

 

[Shafikae]

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 :(

 

[jambaugh]

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.

 

[tune123]

Schaefer would be displeased!

 

[Shafikae]

I got it thank you!