The primary structure of a proposed space stationconsists of fi ve spherical shells

Chapter 7, Problem 7/111

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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 precesses about the Z-axis of fixed orientation and makes a very small angle with it, calculate the rate \(\dot{\psi}\) at which the station wobbles. The mass center O has negligible acceleration.

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