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.
|Journal or Publication Title:||SIAM Journal on 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:||13 Jan 2016 14:53|
Actions (login required)