Nixon, Anthony 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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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.
|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|
|Deposited On:||26 Oct 2012 13:08|
|Last Modified:||25 Sep 2014 08:55|
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