I am having problems figuring out this problem. A rigid body having an axis of symmetry rotates freely about a fixed point under no torques. If alpha is the angle nbetween the axis of symmetry and hte instantous axis of rotaiton, show that he angle between the axis of rotaiton(omega) and the invariable line(L) is tan^-1((Is-I)*tan(alpha)/(Is+ I*tan(alpha)^2)).(adsbygoogle = window.adsbygoogle || []).push({});

Using Euler equations:

omega y'=omega*sin(alpha)

omega z'=omega*cos(alpha)

Ly'=I*omega*sin(alpha)

Lz'=Is*omega*cos(alpha)

and Ly'/Lz'=tan(theta)=I/Is=tan(alpha)

Would the cross product of omega and L give me the angle between the axis of rotation and the invariable line? I am not sure how to begin this problem or if this is the right start.

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# Homework Help: Rigid body motion

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