NDLI: Closed Rotation Sequences

Content Provider	Springer Nature Link
Author	Bhat, Sanjay P. Crasta, Naveena
Copyright Year	2014
Abstract	A finite sequence of rotations is closed if a sequential application of all the rotations from the sequence results in no net orientation change. A complete characterization of closed rotation sequences involving a given set of rotation axes is presented, and the set of such sequences is shown to be a smooth manifold under a nondegeneracy condition on the rotation axes. The characterization is used to derive several examples of closed rotation sequences, some of which are then shown to specialize to classical examples of such sequences provided by the Rodrigues–Hamilton theorem and the Donkin’s theorem. Discrete versions of the Goodman–Robinson and Ishlinskii theorems are also derived and illustrated using the so-called Codman’s paradox.
Ending Page	396
Page Count	31
Starting Page	366
File Format	PDF
ISSN	01795376
e-ISSN	14320444
Journal	Discrete & Computational Geometry
Issue Number	2
Volume Number	53
Language	English
Publisher	Springer US
Publisher Date	2014-12-17
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Codman’s paradox Rotation sequences Ishlinkskii’s theorem Computational Mathematics and Numerical Analysis Rodrigues–Hamilton theorem Donkin’s theorem Orthogonal and unitary groups Goodman–Robinson theorem Kinematics of a rigid body Combinatorics Spherical polygons
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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