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# hw1 - AE3521 Fall 2004 Homework#1 Due Thursday September 2...

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AE3521 Fall 2004 Homework #1 Due: Thursday September 2, 2004 at noon (beginning of class) or before 1. (review problem) Consider the system described by: [ ] = + = 2 1 2 1 2 1 1 1 1 1 1 3 1 4 x x y u x x x x & & (a) Identify A (system matrix), B (input matrix), and C (output matrix) of the system. (b) Obtain a differential equation in terms of ( ) t y and ( ) t u . (c) Obtain a transfer function for the system and find the poles. (d) Determine the eigenvalues of the system matrix and the transfer function poles. 2. Wiesel chapter 1, problem 5, p. 40. 3. The time derivatives of unit vectors i b r (which rotate with angular velocity ω r ) are found by: i i b b dt d r r r × = ω Use this result to show: v v dt d v dt d bi b i r r r r × + = ω where the angular velocity of the b frame with respect to the i frame is bi ω r . 4.
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