# A compact formula for the derivative of a 3-D rotation in exponential coordinates

arXiv: https://arxiv.org/abs/1312.0788 · HTML: https://mlsanity.com/paper/1312.0788/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2013.

## Built on by (most cited first, 14 of 14)

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## Abstract (arXiv)

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.