In Section 8.6.2, we showed that for a free symmetric top, the angular momentum L, the angular velocity , and the symmetry axis x 3

In Section 8.6.2, we showed that for a free symmetric top, the angular momentum L, the angular velocity ω, and the symmetry axis x₃ all lie in a plane. Let α be the angle between x₃ and L, and let β be the angle between x₃ and ω (see Fig.). Find the relationship between α and β in terms of the principal moments, I and I₃.

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