Coning, symmetry, and spherical frameworks

Schulze, Bernd and Whiteley, Walter (2012) Coning, symmetry, and spherical frameworks. Discrete and Computational Geometry, 48 (3). pp. 622-657. ISSN 0179-5376

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Abstract

In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning (Whiteley in Topol. Struct. 8:53–70, 1983), (b) the further transfer of these results to spherical space via associated rigidity matrices (Saliola and Whiteley in arXiv:0709.3354, 2007), and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix (Schulze and Whiteley in Discrete Comput. Geom. 46:561–598, 2011). Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric Md and the hyperbolic metric ℍ d . This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among Ed , cones in Ed+1 , Sd , Md , and ℍ d . We also consider the further extensions associated with the other Cayley–Klein geometries overlaid on the shared underlying projective geometry.

Item Type:
Journal Article
Journal or Publication Title:
Discrete and Computational Geometry
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
63626
Deposited By:
Deposited On:
24 Apr 2013 09:05
Refereed?:
Yes
Published?:
Published
Last Modified:
13 May 2020 02:07