Concept explainers
The essential features of the gyrocompass are shown. The rotor spins at the rate
(a) Show that the equations of motion of the gyrocompass are
where ωz is the rectangular component of the total angular velocity ω along the axis of the rotor, and I and I′ are the moments of inertia of the rotor with respect to its axis of symmetry and a transverse axis through O, respectively.
(b) Neglecting the term containing
and that the axis of the gyrocompass oscillates about the north–south direction.
Fig. P18.158
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Vector Mechanics for Engineers: Statics and Dynamics
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