Chapter4_21

# 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 φ z about the z-axis. Thus = = z r r z y x r xy xy ) sin( ) cos( φ φ r and = = z r r z y x r xy xy ) ' sin( ) ' cos( ' ' ' ' φ φ 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 φ φ φ φ φ φ φ φ φ − = − = + = = ) sin( ) cos( ) sin( ) cos( ) cos( ) sin( ) sin( ) ' sin( ' z z z xy z xy z xy xy x y r r r r y φ φ φ φ φ φ φ φ φ + = + = + = = r R r z z r r ) ( ' φ = where − = z y x z y x z z z z 1 ) cos( ) sin( ) sin( ) cos(...
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## This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

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