p09fl26 - Lecture 26: Top with gravity (2 Nov 09) A....

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Unformatted text preview: Lecture 26: Top with gravity (2 Nov 09) A. Review: Euler angles 1. Three successive rotations to get to the principal axes of the moment of inertia tensor: (1) by angle around the original z = e 3 , (2) rotation by angle around the new y = 2 axis, (3) rotate by angle around the new (and final) z axis e 3 . 2. The final result after matrix multiplication for the successive rotations C ( ) B ( ) A ( ) is CBA = C C C - S S C C S + S C - C S - S C S - C S - S C S + C C S S S C S S C using a notation C = cos , S = sin , etc. 3. Express rotation axes in terms of the principal axes (a) Rotation for (= symmetry axis of the symmetric top) is e e 3 . (b) Rotation for e = e 3 and can express that in terms of the final axes by the transform: (so e 3 e 3 = C ) e = CBA 1...
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p09fl26 - Lecture 26: Top with gravity (2 Nov 09) A....

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