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Rigidity of frameworks supported on surfaces

Nixon, A. and Owen, J. C. and Power, Stephen (2012) Rigidity of frameworks supported on surfaces. SIAM Journal of Discrete Mathematics, 26 (4). pp. 1733-1757. ISSN 0895-4801

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    Abstract

    A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.

    Item Type: Article
    Journal or Publication Title: SIAM Journal of Discrete Mathematics
    Uncontrolled Keywords: bar-joint framework ; framework on a surface ; rigid framework
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 59494
    Deposited By: ep_importer_pure
    Deposited On: 26 Oct 2012 13:08
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:40
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/59494

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