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

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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.

Item Type:
Journal Article
Journal or Publication Title:
SIAM Journal on Discrete Mathematics
Uncontrolled Keywords:
?? bar-joint frameworkframework on a surface rigid frameworkmathematics and statisticsmathematics(all)qa mathematicsdiscipline-based research ??
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Deposited On:
26 Oct 2012 12:08
Last Modified:
24 Apr 2024 00:33