Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
Reference27 articles.
1. Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd edn. Addison-Wesley, Reading (1978)
2. Abraham, R., Marsden, J.E., Raiţu, T.S.: Manifolds, Tensor Analysis, and Applications, 3rd edn. Springer, New York (2002)
3. Amir, D.: Characterizations of Inner Product Spaces. Operator Theory: Advances and Applications, vol. 20. Birkhäuser, Basel (1986)
4. Asimow, L., Roth, B.: The rigidity of graphs. Trans. Am. Math. Soc. 245, 279–289 (1978)
5. Asimow, L., Roth, B.: The rigidity of graphs II. J. Math. Anal. Appl. 68(1), 171–190 (1979)
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