A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates
Author(s)
Gallego, Guillermo
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Abstract
We present a compact formula for the derivative of a 3-D
rotation matrix with respect to its exponential coordinates. A geometric
interpretation of the resulting expression is provided, as well as its
agreement with other less-compact but better-known formulas. To the best of
our knowledge, this simpler formula does not appear anywhere in the
literature. We hope by providing this more compact expression to alleviate
the common pressure to reluctantly resort to alternative representations in
various computational applications simply as a means to avoid the complexity
of differential analysis in exponential coordinates.
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Date
2014-08
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Text
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Pre-print