ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 51, 52, 73 Kovalev, Mikhail, Moscow State University of Forestry, Russia Stability of hinged schemes and frameworks. The geometric properties of hinged constructions in R^{d} (d ≥ 2) are considered. This constructions consist of rigid rods, connected with each other and with some fixed points of the space by hinges, assuming any mutual rotations. A (kinematic) hinged scheme is the graph of such construction together with the collections of positions of its fixed hinges and lengths of its rods. A concept of stability of hinged schemes and frameworks is analyzed. Unsolved problems are stated. Among them is a conjecture about the instability of a scheme, admitting only one framework. Reference: M. D. Kovalev, Geometric theory of hinged devices, Russian Acad. Sci. Izv. Math. 44 (1995), 1, 43-68.