Rotations in three, four, and five dimensions

2011/03/08 by Jason Hanson, Hanson, Jason
Mathematics · Physics and Astronomy · #15B10 #Experimental and Theoretical Physics Studies #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:15B10

paper · pdf · doi:10.48550/arxiv.1103.5263

arxiv created 2011/03/08 · openalex publication_date 2011/03/08 · arxiv updated 2011/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these dimensions.

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• The Gibbs Representation of 3D Rotations
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• Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations
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