The primary structure of a proposed space station consists of five spherical shells connected by tubular spokes.

Question:

The primary structure of a proposed space station consists of five spherical shells connected by tubular spokes. The moment of inertia of the structure about its geometric axis A-A is twice as much as that about any axis through O normal to A-A. The station is designed to rotate about its geometric axis at the constant rate of 3 rev/ min. If the spin axis A-A processes about the Z-axis of fixed orientation and makes a very small angle with it, calculate the rate ψ˙ at which the station wobbles. The mass center O has negligible acceleration.