Article: Generalized polar coordinates on Lie groups and numerical integrators
Authors: Stein Krogstad · Hans Z. Munthe-Kaas · Antonella Zanna
Journal:NUMERISCHE MATHEMATIK Volume 114, Number 1 (2009), 161-187.
Abstract: Motivated by developments in numerical Lie group integrators, we introduce a family of local coordinates on Lie groups denoted generalized polar coor- dinates. 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.
Hindsight notes: For non-scientific reasons it took six years to publish this work! (My fault!).
18 Aug 2008