p09fl25 - Lecture 25: Euler angles (30 Oct 09) A. Euler...

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Unformatted text preview: Lecture 25: Euler angles (30 Oct 09) A. Euler angles 1. FW sec 29. Start from a set of (inertial) Cartesian axes ( e 1 , e 2 , e 3 ) 2. 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 . [This is the conventional set for QM angular momentum; classical mechanics texts such as Goldstein use the x axis for the second rotation] 3. 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. 4. Naming of axes: (a) Rotation axis for (about the symmetry axis of the symmetric top) is e e 3 . (b) rotation for was the original e 3 and can express that in terms of the final axes by the transform: (so e 3 e 3 = C ) e = CBA 1 =- C...
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.

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p09fl25 - Lecture 25: Euler angles (30 Oct 09) A. Euler...

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