The spacecraft shown has a mass m with mass centerG. Its radius of gyration about its

Chapter 7, Problem 7/68

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The spacecraft shown has a mass m with mass center G. Its radius of gyration about its z-axis of rotational symmetry is k and that about either the x- or y-axis is \(k^{\prime}\). In space, the spacecraft spins within its x-y-z reference frame at the rate \(p=\dot{\boldsymbol{\phi}}\). Simultaneously, a point C on the z-axis moves in a circle about the \(z_{0} \text {-axis }\) with a frequency ƒ (rotations per unit time). The \(z_{0} \text {-axis }\) has a constant direction in space. Determine the angular momentum \(\mathbf{H}_{G}\) of the spacecraft relative to the axes designated. Note that the x-axis always lies in the \(z-z_{0}\) plane and that the y-axis is therefore normal to \(z_{0}\).