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Unformatted text preview: Lecture 6: Rotations I (16 Sep 09) 0. review homework The homework is posted and can be accessed from the below link, after login to MyUW to view the contents. https://www.library.wisc.edu/course-pages/viewer/show/1537 A. Rotation of coordinate axes 1. Rotate axes x,y by angle about the z axis. The original orientation has subscript 0: x = x cos - y sin ; y = x sin + y cos with inverse relation x = x cos + y sin ; y = x sin + y cos 2. vector notation: boldface lower case is vector; boldface upper case is matrix: r = M r ; r = M T r 3. The notation M T denotes transpose. These are orthogonal matrices: the transpose is equal to the inverse (ck). 4. Rotate by angle about an arbitrary axis n (G, Sec. 4.7) (a) The component of r parallel to n is unaffected. r k = n ( r n ) (b) Before rotation, the component perpendicular to the axis is r , = r- n ( r n ) (c) A second vector perpendicular to this and to n is n r , = n r 1 (d) The rotation analogous to (1) is...
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This note was uploaded on 09/29/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.
- Fall '09