Lancaster EPrints

Rigidity of frameworks supported on surfaces

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

PDF (Rigidity of Frameworks Supported on Surfaces) - Draft Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (299Kb) | Preview


    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: Journal Article
    Journal or Publication Title: SIAM Journal on Discrete Mathematics
    Uncontrolled Keywords: bar-joint framework ; framework on a surface ; rigid framework
    Subjects: ?? qa ??
    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: 22 Jun 2018 00:22
    Identification Number:

    Actions (login required)

    View Item