A spacecraft is launched into a low Earth orbit. The spacecraft principal moments of inertia are Ix = 98 kg.m², Iy = 102 kg.m², Iz = 150 kg.m². For stability, the launch vehicle deploys the spacecraft such that it is in a major axis spin when released, with wz = 0.5 rad/s. Because no deployment is perfect, the spacecraft also has some angular velocity about the other two principal axes, given by w = 0.1 rad/s, wy = 0.02 rad/s. Making appropriate approximations: (a) Describe the resulting spacecraft attitude motion if there are no disturbance torques. (b) Determine the nutation angle. (c) Determine the precession rate.

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1. A spacecraft is launched into a low Earth orbit. The spacecraft principal moments of inertia
are IT = 98 kg.m², Iy 102 kg.m², I₂ = 150 kg.m². For stability, the launch vehicle deploys
the spacecraft such that it is in a major axis spin when released, with wz = 0.5 rad/s. Because
no deployment is perfect, the spacecraft also has some angular velocity about the other two
principal axes, given by we = 0.1 rad/s, wy = 0.02 rad/s. Making appropriate approximations:
(a) Describe the resulting spacecraft attitude motion if there are no disturbance torques.
(b) Determine the nutation angle.
(c) Determine the precession rate.
Transcribed Image Text:Iz 1. A spacecraft is launched into a low Earth orbit. The spacecraft principal moments of inertia are IT = 98 kg.m², Iy 102 kg.m², I₂ = 150 kg.m². For stability, the launch vehicle deploys the spacecraft such that it is in a major axis spin when released, with wz = 0.5 rad/s. Because no deployment is perfect, the spacecraft also has some angular velocity about the other two principal axes, given by we = 0.1 rad/s, wy = 0.02 rad/s. Making appropriate approximations: (a) Describe the resulting spacecraft attitude motion if there are no disturbance torques. (b) Determine the nutation angle. (c) Determine the precession rate.
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