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A compact formula for the derivative of a 3-D rotation in exponential coordinates
lib:f54b5e4d4a90c811 (v1.0.0)
Authors: Guillermo Gallego,Anthony Yezzi
ArXiv: 1312.0788
Document: PDF DOI
Abstract URL: http://arxiv.org/abs/1312.0788v2
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.
ArXiv: 1312.0788
Document: PDF DOI
Abstract URL: http://arxiv.org/abs/1312.0788v2
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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