hw02_FA05 - N(i.e A motor is driving a telescoping arm...

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R.G. Melton AERSP 309 HW #2 Fall 2005 (Due Friday Sept. 16 at beginning of class) 1. Prob. 1, Wiesel, p. 39 2. Prob. 2, Wiesel, p. 39 3. Consider small sounding rockets that are to be launched from each of the following locations: a.) the steps of Old Main, b.) Kennedy Space Center, and c.) Kourou, French Guiana. In each case, calculate the speed of the vehicle just prior to launch in a Newtonian reference frame (i.e., one that does not rotate wrt the stars) with origin at Earth’s center. 4. Prob. 4, Wiesel, p. 39 5. A cylindrical-shaped satellite is rotating at rate about the axis as shown in the figure. At time t = 0, the body-fixed frame B is aligned with the Newtonian frame
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Unformatted text preview: N (i.e., ). A motor is driving a telescoping arm outward along the axis, such that at time t , the mass m at the tip of the arm is located at k BN ω 3 ˆ b 3 , 1 , ˆ ˆ = = i n b i i 1 ˆ b 1 + k 2 (1 - e-β t ) , where β , k 1 ˆ b 1 and k 2 are positive constants. a. Find an expression for the velocity of the mass in the Newtonian frame N, expressed in terms of the vectors , as a function of t . i b ˆ b. Find an expression for the DCM C NB as a function of t . c. Find an expression for the velocity of the mass in the Newtonian frame N, expressed in terms of the vectors , as a function of t . i n ˆ 3 ˆ b 3 ˆ n 2 ˆ b 2 ˆ n 1 ˆ n 1 ˆ b m...
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