The Orbit Rigidity Matrix of a Symmetric Framework |
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Authors: | Bernd Schulze Walter Whiteley |
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Institution: | 1.Institute of Mathematics,MA 6-2 Technische Universit?t Berlin,Berlin,Germany;2.Department of Mathematics and Statistics,York University,Toronto,Canada |
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Abstract: | A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed,
and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid
graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides
a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The
orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights
into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. |
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Keywords: | |
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