6. B6 If precession is unhindered, it is the most significant effect due to applying a torque at right angles to the spin axis, because it will continue until the torque is removed. There is, however, another response to the torque as well. Given an~ at right angles to its~, a gyroscope, besides precessing, will also rotate its spin axis around the torque axis; physically this means that the points of application of the forces will move slightly in the direction of those forces. The situation is shown in Figure 6.B4. Unlike the unopposed precession, this deflection of the spin axis around the torque axis is resisted by the gyro which behaves like a torsional spring with torsional stiffness given by: - H2 (Torsional stiffness) - I y (6. Bl) where Iy is the moment of inertia of the gyro about a transverse axis. Thus the deflection angle is governed by the equation: L (6. Bl) This leads to simple harmonic motion when Lis constant. If the oscillations are dam?ed out: I L J_ asteady state= 8 2
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