The pilot can achieve any groundspeed by p ointing

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Unformatted text preview: −2t � �(t) = 0 e−2t −1 1 s+1 − 1 s+2 1� s+2 We are given the initial conditions � (0) and the input u(t), so we can calculate the state vector at x any time t > 0: ⎥ t � (t) = �(t)� (0) + x x �(t − � )B� (� )d� u 0 � −t −t � � � ⎥ t � −(t−� ) −(t−� ) �� � e e − e−2t 1 e e − e−2(t−� ) 0 = + (1)d� 0 e−2t 1 1 0 e−2(t−� ) 0 � ⎥ t � −(t−� ) � −t � 2e − e−2t e − e−2(t−� ) = + d� e−2t e−2(t−� ) 0 � � −(t−� ) 1 −2(t−� ) �� =t � −t e − 2e 2e − e−2t + = 1 −2(t−� ) e−2t 2e � � =0 � �1 � −t 1 −2t 2e − e − e−t + 2 e−2t = + 2 1 1 −2t −e e2t �1 �2 2 −t − e−2t ) 2 (1 + 2e = 1 −2t )...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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