p605hw7f08wsoln - Phys 605. Homework 7 Due 5pm, Monday,...

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Phys 605. Homework 7 Due 5pm, Monday, November 3, 2008 Problem 7-1: [10 pts] Make sure you understand the derivation of the “active” rotation formula (Eq. 4.62 GPS pg. 162) r 0 = r cosΦ + ˆn ( r · )(1 - cosΦ) + ( r × )sinΦ . ( “active” rotation formula ) that expresses r 0 obtained by rotating r about an axis along = n 1 ˆ x 1 + n 2 ˆ x 2 + n 3 ˆ x 3 (where n 2 1 + n 2 2 + n 2 3 = 1) by angle Φ, where we take positive Φ to be in the negative Right Hand Rule (R.H.R.) sense around (as shown in Fig. 4.8 in GPS pg. 162) because we want to use this “active” transformation to obtain the corresponding “passive” coordinate transformation below. (a) Use the “active” rotation formula to show the general rotation matrix A , ) representing the “passive” co- ordinate transformation for a coordinate rotation by angle Φ ( positive R.H.R.) about an axis along is given by: A = n 2 1 (1 - cosΦ) n 1 n 2 (1 - cosΦ) + n 3 sinΦ n 1 n 3 (1 - - n 2 n 2 n 1 (1 - - n 3 n 2 2 (1 - n 2 n 3 (1 - cosΦ) + n 1 n 3 n 1 (1 - cosΦ) + n 2 n 3 n 2 (1 - - n 1 n 2 3 (1 - .
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This note was uploaded on 02/09/2012 for the course PHYS 605 taught by Professor Staff during the Fall '09 term at Ohio University- Athens.

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p605hw7f08wsoln - Phys 605. Homework 7 Due 5pm, Monday,...

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