Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_101

7/101 The spacecraft shown is symmetrical about its $z$-axis and has a radius of gyration of $720 \text{ mm}$ about this axis. The radii of gyration about the $x$- and $y$-axes through the mass center are both equal to $540 \text{ mm}$. When moving in space, the $z$-axis is observed to generate a cone with a total vertex angle of $4^\circ$ as it precesses about the axis of total angular momentum. If the spacecraft has a spin velocity $\dot{\phi}$ about its $z$-axis of $1.5 \text{ rad/s}$, compute the period $\tau$ of each full precession. Is the spin vector in the positive or negative $z$-direction?