Revision as of 19:11, 15 January 2024 edit 71.249.111.125 (talk) →Order of rotations ← Previous edit		Revision as of 19:32, 15 January 2024 edit undo Jacobolus (talk \| contribs) Extended confirmed users 40,160 edits →Order of rotations: name and wikilink the BCH formula Next edit →
Line 83: again to first order. In other words, {{em\|the order in which infinitesimal rotations are applied is irrelevant}}. This useful fact makes, for example, derivation of rigid body rotation relatively simple. But one must always be careful to distinguish (the first order treatment of) these infinitesimal rotation matrices from both finite rotation matrices and from Lie algebra elements. When contrasting the behavior of finite rotation matrices in the ~~BCH (acronym is heretofore undefined. Please define)~~[[Baker–Campbell–Hausdorff formula]] above with that of infinitesimal rotation matrices, where all the commutator terms will be second order infinitesimals one finds a bona fide vector space. Technically, this dismissal of any second order terms amounts to [[Group contraction]]. == Generators of rotations ==

Infinitesimal rotation matrix: Difference between revisions