Infinitesimally Rigid Polyhedra. I. Statics of Frameworks

DOI10.2307/1999446zbMath0518.52010OpenAlexW4233204492MaRDI QIDQ3667516

Walter J. Whiteley

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999446

zbMATH Keywords

convex polyhedrainfinitesimal rigiditybar and joint frameworksstatic rigidity

Mathematics Subject Classification ID

Kinematics of mechanisms and robots (70B15) Polytopes and polyhedra (52Bxx)

Related Items

Rigidity of ball-polyhedra in Euclidean 3-space, Zero temperature limit for interacting Brownian particles. I: Motion of a single body., Skeletal rigidity of simplicial complexes. I, Skeletal rigidity of simplicial complexes. II, Linking (n-2)-dimensional panels in n-space. II: (n-2,2)-frameworks and body and Hinge structures, Mechanics of materials with periodic truss or frame micro-structures, The generic rigidity of triangulated spheres with blocks and holes, Addressing agent loss in vehicle formations and sensor networks, Bending of surfaces. II, Finite and infinitesimal rigidity with polyhedral norms, Strict Kneser-Poulsen conjecture for large radii, Reconstructing simplicial polytopes from their graphs and affine 2-stresses, Tensegrity Frameworks, Graph rigidity for unitarily invariant matrix norms, The orbit rigidity matrix of a symmetric framework, On the number of realizations of certain Henneberg graphs arising in protein conformation, Tensegrity frameworks: static analysis review, A lower bound theorem for centrally symmetric simplicial polytopes, Generic rigidity of molecular graphs via ear decomposition, The rigidity of infinite graphs, Rigidity and the Alexandrov-Fenchel inequality, On traces of \(d\)-stresses in the skeletons of lower dimensions of piecewise-linear \(d\)-manifolds, Rigidity and the lower bound theorem. I, On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs, Unnamed Item, On Kalai's conjectures concerning centrally symmetric polytopes, Almost Simplicial Polytopes: The Lower and Upper Bound Theorems, Projective background of the infinitesimal rigidity of frameworks, The Colin de Verdière number and sphere representations of a graph, Inner diagonals of convex polytopes, How to describe or design a polyhedron, A homological interpretation of skeletal ridigity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The rigidity of graphs. II
• The rigidity of certain cabled frameworks and the second-order rigidity of arbitrary triangulated convex surfaces
• When is a bipartite graph a rigid framework?
• Graßmann angles of convex polytopes
• The Algebraic Geometry of Stresses in Frameworks
• The Rigidity of Polyhedral Surfaces
• Rigid and Flexible Frameworks
• Tensegrity Frameworks
• Geometrical problems concerning polyhedra in the large