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HW4 - MAE146 Astronautics Homework Assigned Friday January...

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MAE146: Astronautics – Homework Assigned: Friday, January 15 th , 2010 Due date: Wednesday , January 20 th , 2010, (at the beginning of the lecture) Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget to write your name on your copy to receive credit. Problem 1 (15pts): Still on Angular Velocity In class, we have written (and proved) the kinematic differentiation rule: bracketleftbigg vectoru dt bracketrightbigg 1 = bracketleftbigg vectoru dt bracketrightbigg 2 + vectorω × vectoru (1) by using vector coordinates expressed in the moving frame (frame 2): ˙ ¯ x ˙ ¯ y ˙ ¯ z = R. ˙ x ˙ y ˙ z - Q. ¯ x ¯ y ¯ z (2) where ( x,y,z ) and (¯ x, ¯ y, ¯ z ) represent the coordinates of vectoru in the first frame and second frames, respectively, R denotes the rotation matrix between the first and second frame and Q is a matrix representation of the cross product with

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