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Eulerian angles
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Eulerian angles
Eulerian angles
4.21 A dumbbell-shaped spacecraft (two masses m connected by a weightless bar of length L as shown in Fig. P4.21) is subjected to the influence of an inverse square gravity field of the Earth. The circular orbit of the center of mass has a semimajor axis of 7000 km. Express all vectors in the orbit frame O: {êr, ĉo, în}. (a) Derive the gravity gradient torque for this simple two-dimensional spacecraft model about the craft center of mass. Have O be the angle of the craft with respect to nadir. (b) With m=100 kg and L=10m, plot the gravity gradient torque magnitude for 1/2 <O< 1/2. (c) Assume an atmospheric torque of 1 = 2 x 10 3Nm is acting on the body. At what torque equilibrium angle (TEA) Otea will the gravity gradient torque cancel the atmospheric torque? m Ti 0 le RC T2 m Fig. P4.21 Dumbbell spacecraft illustration.
4.21 A dumbbell-shaped spacecraft (two masses m connected by a weightless bar of length L as shown in Fig. P4.21) is subjected to the influence of an inverse square gravity field of the Earth. The circular orbit of the center of mass has a semimajor axis of 7000 km. Express all vectors in the orbit frame O: {êr, ĉo, în}. (a) Derive the gravity gradient torque for this simple two-dimensional spacecraft model about the craft center of mass. Have O be the angle of the craft with respect to nadir. (b) With m=100 kg and L=10m, plot the gravity gradient torque magnitude for 1/2 <O< 1/2. (c) Assume an atmospheric torque of 1 = 2 x 10 3Nm is acting on the body. At what torque equilibrium angle (TEA) Otea will the gravity gradient torque cancel the atmospheric torque? m Ti 0 le RC T2 m Fig. P4.21 Dumbbell spacecraft illustration.