Chapter4_21 - PHY4604 R. D. Field Department of Physics...

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Unformatted text preview: PHY4604 R. D. Field Department of Physics Chapter4_21.doc University of Florida Rotations in 3 Dimensional Space (1) Rotations About the z-Axis: Rotate the vector r r by an angle z about the z-axis. Thus = = z r r z y x r xy xy ) sin( ) cos( r and = = z r r z y x r xy xy ) ' sin( ) ' cos( ' ' ' ' r where 2 2 2 2 ' ' y x y x r xy + = + = and ) sin( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( ) ' cos( ' z z z xy z xy z xy xy y x r r r r x = = + = = ) sin( ) cos( ) sin( ) cos( ) cos( ) sin( ) sin( ) ' sin( ' z z z xy z xy z xy xy x y r r r r y + = + = + = = r R r z z r r ) ( ' = where = z y x z y x z z z z 1 ) cos( ) sin( ) sin( ) cos(...
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