Abstract
Motivated by developments in numerical Lie group integrators, we introduce a family of local coordinates on Lie groups denoted generalized polar coordinates. Fast algorithms are derived for the computation of the coordinate maps, their tangent maps and the inverse tangent maps. In particular we discuss algorithms for all the classical matrix Lie groups and optimal complexity integrators for n-spheres.
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Krogstad, S., Munthe-Kaas, H.Z. & Zanna, A. Generalized polar coordinates on Lie groups and numerical integrators. Numer. Math. 114, 161–187 (2009). https://doi.org/10.1007/s00211-009-0255-1
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DOI: https://doi.org/10.1007/s00211-009-0255-1