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Unformatted text preview: TEXAS A&M UNIVERSITY Department of Mechanical Engineering MEEN 431 Advanced System Dynamics and Controls Spring 2009 Homework I – due Tuesday, February 4, 2009 1. Show that R x ( θ ) = 1 cos θ- sin θ sin θ cos θ , R y ( φ ) = cos φ sin φ 1- sin φ cos φ . (1) 2. A material particle P initially with co-ordinates (1 , , 0) is rotated about the I axis through an angle of π 4 radians followed by a rotation about the J axis through an angle of π 3 radians. What are the new coordinates of the particle? What would the coordinates be if the order of rotations were reversed? 3. Let θ, φ, ψ be small angles, i.e., they are all smaller than in magnitude, with being close to zero. Suppose one were to rotate a particle about the I axis through an angle θ , about the J axis through an angle φ and through the K axis through an angle ψ . • For any sequence in which the point is rotated about the I, J and K axes, show that the resulting rotation matrix is of the form: R ( θ, φ, ψ ) = 1 1 1 + - 1 1 θ + 1...
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This note was uploaded on 09/10/2009 for the course MEEN MEEN612 taught by Professor Swaroopdarbha during the Spring '09 term at Texas A&M.
- Spring '09