Rigidity And Tensegrity By Connelly
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Rigidity And Tensegrity in Tensegrity structures
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Rigidity And Tensegrity By Connelly
- 1. Rigidity and Tensegrity Robert Connelly Cornell University
- 2. Part I: The local theory Statics
- 8. What model?
- 10. What sort of rigidity/stablility?
- 12. What energy function to choose?
- 17. An example of a stress matrix
- 20. Part II: The global theory Stress matrices applied again.
- 23. How do you tell when a given framework is globally rigid?
- 27. Part III: Bar frameworks More stress matrices using the generic philosophy.
- 38. Proof that the stress condition implies global rigidity The Tarski-Seidenberg theory of quantifier elimination implies that the situation below cannot happen, since the configuration p is generic. So a neighborhood of p can be mapped to a neighborhood of q by a diffeomorphism h, so that fh = f, and df p = df q dh p . This implies that any equilibrium stress for p is an equilibrium stress for q . If the rank of the associated stress matrix is maximal, this implies that p and q are affine images of each other, and ultimately that they are congruent.
- 49. An example of the Berg-Jordan Henneberg transformations
- 50. An example of the Berg-Jordan Henneberg transformations
- 51. An example of the Berg-Jordan Henneberg transformations
- 52. An example of the Berg-Jordan Henneberg transformations
- 53. An example of the Berg-Jordan Henneberg transformations
- 54. An example of the Berg-Jordan Henneberg transformations
- 55. An example of the Berg-Jordan Henneberg transformations
- 57. Part IV: Existence of realizations When does a graph have a realization with predermined edge lengths?