This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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/coursepages/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...
View
Full
Document
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
 BRUCH
 Work

Click to edit the document details