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MIT16_07F09_hw12

# MIT16_07F09_hw12 - NAME Massachusetts Institute of...

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 12 Out date: Nov. 21, 2007 Due date: Nov. 30, 2007 Time Spent [minutes] Problem 1 Problem 2 Study Time Turn in each problem on separate sheets so that grading can be done in parallel

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MATLAB Problem 1 (20 points) In problem set 2, you performed a coordinate transformation to align your coordinate system with the upper edge of a unit cube, the point 1,1,1. The transformation matrix was the product of the transformation matrices for each step in the process: counterclockwise rotation θ = π/ 4 about z to obtain the x y z ; a clockwise rotation ψ = tan 1 1 2 about y to obtain the x �� , y �� , z �� coordinate system. The final transformation matrix was cosψcosθ cosψsinθ sinψ . 5774 . 5774 . 5774 [ T ] = sinθ cosθsinψ cosθ sinψsinθ 0 cosψ = 0 . 7071 0 . 4082 0 . 7071 0 . 4082 0 0 . 8165 (1) The inertia matrix for a cube about the origin in the x, y, z system is 2 / 3 1 / 4 1 / 4 Mb 2 1 / 4 2 / 3 1 / 4 (2) 1 / 4 1 / 4 2 / 3 .
a) Using MATLAB, apply the transformation matrix generated by the transformation to transform the inertia tensor/matrix of the cube. Show that the axes in the coordinate system x �� , y �� , z �� are

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MIT16_07F09_hw12 - NAME Massachusetts Institute of...

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