Heavy Symmetric Top: Obtain Euler Equation Condition

[Zeroxt]

Hi, I have another problem:

Obtain from the Euler equations the condition:

These condition for a uniform precession of a heavy symmetric top, imposing that the condition of motion have to be a uniform precession without nutation.

I don't know which precisely is the condition to obtain the equation exposed before.
I hope you can help me.

 

[Asim Riaz]

The condition for a uniform precession of a heavy symmetric top is that the angular momentum vector must remain constant. This can be expressed mathematically by taking the time derivative of the angular momentum vector to be equal to zero, ordL/dt = 0This condition is equivalent to the Euler equations, which state that the time derivatives of the Euler angles are related bydΦ/dt = I₁ ⋅ dL/dt / I₃,dθ/dt = I₂ ⋅ dL/dt / I₃,dφ/dt = (I₁ - I₂) ⋅ dL/dt / I₃,where I₁, I₂ and I₃ are the moments of inertia of the body about the principal axes. Thus, for a uniform precession of a heavy symmetric top, the Euler equations reduce todΦ/dt = 0,dθ/dt = 0,dφ/dt = 0.