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Unformatted text preview: Physics 409/Classical Mechanics Test #4 4 November 2010 Name ANSWERS Answer all parts of each of the two questions. 50 points total. The points value of each part is indicated. Begin the answer to each question on a new sheet of paper. Clearly define all coordinates and variables. Be sure to include sufficient detail in each answer so that your logic is clear to me. Reminder: The standard 2×2 orthogonal matrix for a counterclockwise coordinate rotation in a plane through an angle α is . cos sin sin cos α α α α ⎛ ⎞ ⎜ ⎟ − ⎝ ⎠ (1) (25 pts.) The Euler angles are defined in Goldstein by the following operations: (1) A rotation through the angle φ about the space z axis produces intermediate axes ξ , η , ζ . (2) A rotation through the angle θ about the ξ (intermediate x ) axis produces new intermediate axes ξ N , η N , ζ N . (3) A rotation through the angle ψ about the ζ N (new intermediate z ) axis produces body axes x N , y N , z N . (a)(9 points) Find the 3×3 matrices D ( φ ), C ( θ ), and B ( ψ ) from which the overall Euler matrix A can be calculated as A = BCD . The matrix A transforms space frame components into body frame components: x N = A x . You do not have to calculate ....
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.
- Fall '10