The exponential map that takes skew symmetric matrices to rotation matrices is simply the matrix exponential over a linear combination of the generators:
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(95) |
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(96) | |
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(97) |
The resulting elements form the Taylor series expansion of
and
:
![]() |
(98) |
Thus the exponential map yields a rotation by radians.
The exponential map can be inverted, going from
to
:
Ethan Eade 2012-02-16