Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces

Dewar, S. (2019) Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces. Discrete and Computational Geometry. ISSN 0179-5376

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Abstract

We present a rigorous study of framework rigidity in general finite dimensional normed spaces from the perspective of Lie group actions on smooth manifolds. As an application, we prove an extension of Asimow and Roth’s 1978/1979 result establishing the equivalence of local, continuous and infinitesimal rigidity for regular bar-and-joint frameworks in a d-dimensional Euclidean space. Further, we obtain upper bounds for the dimension of the space of trivial motions for a framework and establish the flexibility of small frameworks in general non-Euclidean normed spaces.

Item Type:
Journal Article
Journal or Publication Title:
Discrete and Computational Geometry
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
138797
Deposited By:
Deposited On:
11 Nov 2019 13:55
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Mar 2020 06:51