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hw11_FA05

# hw11_FA05 - R.G Melton Fall 2005 AERSP 309 HW#11(Due Monday...

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R.G. Melton AERSP 309 HW #11 Fall 2005 (Due Monday Dec. 5 at beginning of class) 1. (20 points) Consider a rigid body with principal moments of inertia I 1 = I 2 = 5000 kg m 2 and I 3 = 9000 kg m 2 . It is rotating in a torque-free environment, with initial conditions ω 1,0 = 0.2 rad/s, 2,0 = 0.35 rad/s, and 3,0 = 2.7 rad/s. a. (10 pts) Find the complete solutions for 1 ( t ), 2 ( t ), and 3 ( t ). b. (5 pts) Calculate the angle between 3 ˆ and b K c. (5 pts) Show that 3 ˆ and , , b H K K all lie in the same plane at any time. Remember that 3 vectors are coplanar if any one of them is perpendicular to a vector created by the cross product of the other two original vectors. 2. (20 points) A satellite that is spinning about its 3 ˆ b -axis is initially oriented with 3 3 ˆ to parallel ˆ n b in the Newtonian frame as shown in the figure. Mission requirements call for reorienting the s/c by 30 deg. about the 2 ˆ n -axis. This is to be accomplished by

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hw11_FA05 - R.G Melton Fall 2005 AERSP 309 HW#11(Due Monday...

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