Unformatted text preview: (b) Repeat for a rotation of 45 o about the zaxis followed by a rotation of 30 o about the xaxis. 5. Show that exp( ε A )exp( B ) = exp( A + B + 2 2 [ A , B ] + O ( 3 )) where A and B are matrices and is small. 6. The square has an eightelement symmetry group of rotations and reflections. (a) Write down a set of 2 × 2 matrices representing this group. Is this group commutative (Abelian)? (b) Give names to the 8 elements and construct their multiplication table. Verify that the product of any two reflections is a rotation. (c) How many elements are in the symmetry group of the cube?...
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 Fall '08
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 mechanics, Rotation

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