A spin stabilized spacecraft separates from the upper stage of a booster. Gyros on the freely precessing
(torque free) spacecraft measure a constant spin rate of 72 deg/sec (12 rpm) along the 𝐛3 axis. The
transverse component of co rotates in the 𝐛1 − 𝐛2 plane; it has a magnitude of 𝜔𝑇 = 7.87 deg/sec. The
spacecraft is symmetric about its spin axis, which is aligned with 𝐛3. The spin moment of inertia is C =
1000 𝑠𝑠 − 𝑓𝑡2 and the transverse moment of inertia is A = 700 𝑠𝑠 − 𝑓𝑡2.
a) What is the amplitude of wobble in degrees?
b) What is the nutation angle amplitude in degrees?
c) What is the magnitude of the angular momentum vector in ft-lb-sec?
d) Describe the orientation of the angular momentum vector with respect to the cone swept out by the
spin axis as viewed by an inertially fixed observer.
e) Is the momentum vector constant to a spacecraft-fixed observer?
f) An external (inertially fixed) observer sees the spin axis sweep out an inertially fixed cone. At what
rate does the spin axis rotate about the cone's centerline?
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