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Re-Orient a Sphere with Two Straight Rolls

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longitude θ
0
latitude ϕ
0
twist ψ
1.5708
path progress
0.2
It is well-known that a sphere can be rolled in the horizontal plane to any orientation by three sequentially orthogonal rolls. This Demonstration shows that only two straight rolls are necessary. The desired orientation, shown in red, is specified by moving the north pole to a desired latitude
θ
and longitude
ϕ
, then twisting about this pole by
ψ
. Rolling from the initial orientation, shown in green, along the blue and red lines brings the sphere to the desired orientation.
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