A proposed space station is closely approximated by four uniform spherical shells, each of mass \(m\) and radius \(r\). The mass of the connecting structure and internal equipment may be neglected as a first approximation. If the station is designed to rotate about its \(z\)-axis at the rate of one revolution every 4 seconds, determine \((a)\) the number \(n\) of complete cycles of precession for each revolution about the \(z\)-axis if the plane of rotation deviates only slightly from a fixed orientation, and (b) find the period \(\tau\) of precession if the spin axis \(z\) makes an angle of \(20^{\circ}\) with respect to the axis of fixed orientation about which precession occurs. Draw the space and body cones for this latter condition.

Transcribed Image Text:

Z 2 x