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Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces. / Dewar, S.
In: Discrete and Computational Geometry, Vol. 65, 30.04.2021, p. 655–679.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dewar, S 2021, 'Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces', Discrete and Computational Geometry, vol. 65, pp. 655–679. https://doi.org/10.1007/s00454-019-00135-5

APA

Dewar, S. (2021). Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces. Discrete and Computational Geometry, 65, 655–679. https://doi.org/10.1007/s00454-019-00135-5

Vancouver

Dewar S. Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces. Discrete and Computational Geometry. 2021 Apr 30;65:655–679. Epub 2019 Sept 20. doi: 10.1007/s00454-019-00135-5

Author

Dewar, S. / Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces. In: Discrete and Computational Geometry. 2021 ; Vol. 65. pp. 655–679.

Bibtex

@article{b09fd5fedaae43c3b677320e1da0b123,
title = "Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces",
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{\textquoteright}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.",
keywords = "Bar–joint frameworks, Infinitesimal rigidity, Continuous rigidity, Local rigidity, Finite dimensional normed spaces",
author = "S. Dewar",
note = "The final publication is available at Springer via https://doi.org/10.1007/s00454-019-00135-5",
year = "2021",
month = apr,
day = "30",
doi = "10.1007/s00454-019-00135-5",
language = "English",
volume = "65",
pages = "655–679",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer New York",

}

RIS

TY - JOUR

T1 - Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces

AU - Dewar, S.

N1 - The final publication is available at Springer via https://doi.org/10.1007/s00454-019-00135-5

PY - 2021/4/30

Y1 - 2021/4/30

N2 - 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.

AB - 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.

KW - Bar–joint frameworks

KW - Infinitesimal rigidity

KW - Continuous rigidity

KW - Local rigidity

KW - Finite dimensional normed spaces

U2 - 10.1007/s00454-019-00135-5

DO - 10.1007/s00454-019-00135-5

M3 - Journal article

VL - 65

SP - 655

EP - 679

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

ER -