1. On the admissible dualities in Maxwell’s reciprocal construction
- Author
-
Tamás Baranyai
- Subjects
Pure mathematics ,Diagram (category theory) ,Applied Mathematics ,Mechanical Engineering ,Truss ,Condensed Matter Physics ,Mechanics of Materials ,Modeling and Simulation ,Reciprocity (electromagnetism) ,Duality (projective geometry) ,Projective space ,Projective connection ,General Materials Science ,Projective test ,Reciprocal ,Mathematics - Abstract
In one of his papers Maxwell noted the reciprocity of form and force diagrams of planar trusses and gave a graphical construction relying on a 3 dimensional duality in projective space to get one diagram from the other. While there are numerous different applications and occasional alterations of the method he used and many aspects of this construction are thoroughly analysed, the nature of the projective connection between the two diagrams still remains to be investigated. This paper aims to start such analysis by presenting some basic results on how far the method can be generalized, in terms of admissible projective dualities and projections.
- Published
- 2019