McGill University
PHYS 131
1. (a) Find the rotation matrix for a rotation of 120 about the y-axis followed by a rotation of 45 about the z-axis. (b) Check by explicit calculation that the resulting matrix is orthogonal. 2. (a) Show that the rotation matrix for a combination of the following three rota tions, i. an angle ii. an angle iii. an angle is given by cos cos R= sin cos [02 ) about th
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McGill University
PHYS 131
1. (a) Find the rotation matrix for a rotation of 120 about the y-axis followed by a rotation of 45 about the z-axis. (b) Check by explicit calculation that the resulting matrix is orthogonal. 2. (a) Show that the rotation matrix for a combination of the following three rota tions, i. an angle ii. an angle iii. an angle is given by cos cos R= sin cos [02 ) about the z-axis; [0 ] about the x-axis; [02 ) about the z-axis; sin cos sin cos cos sin cos sin +sin cos cos sin sin sin sin +cos cos cos cos sin sin sin sin cos cos (b) It can be shown that any (proper) rotation can be written on the form above, and the angles are called the three Euler angles. Find the Euler angles corresponding to the rotation in Question 1 above. HINT: Start by determining , in the Rzz component. Then determine and
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