Spherical Unit Vectors in relation to Cartesian Unit Vectors
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Spherical Unit Vectors in relation to Cartesian Unit Vectors
Spherical Unit Vectors in relation to Cartesian Unit Vectors. ˆˆ ˆ, , r θ φ can be
rewritten in terms of ˆ ˆ ˆ, ,. x y z using the following transformations: ˆ. ˆ. ˆ. ˆ sin cos
.
Spherical Unit Vectors in relation to Cartesian Unit Vectors
rˆ , θˆ , φˆ can be rewritten in terms of xˆ , yˆ , zˆ using the following transformations:
rˆ sin cos xˆ sin sin yˆ cos zˆ θˆ cos cos xˆ cos sin yˆ sin zˆ φˆ sin xˆ cos yˆ NOTICE: Unlike xˆ , yˆ , zˆ ; rˆ , θˆ , φˆ are NOT uniquely defined!
The game can be played in reverse to find xˆ , yˆ , zˆ in terms of rˆ , θˆ , φˆ :
xˆ sin cos rˆ cos cos θˆ sin φˆ yˆ sin sin rˆ cos sin θˆ cos φˆ zˆ cos rˆ sin θˆ
