Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_60

7/60 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 \( k' \). In space, the spacecraft spins within its \( x \)-\( y \)-\( z \) reference frame at the rate \( p = \dot{\phi} \). Simultaneously, a point \( C \) on the \( z \)-axis moves in a circle about the \( z_0 \)-axis with a frequency \( f \) (rotations per unit time). The \( z_0 \)-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 \( z_0 \).