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Mat. Sb., 2004, Volume 195, Number 6, Pages 71–98 (Mi msb827)  

This article is cited in 4 scientific papers (total in 4 papers)

Straightened hinged frameworks

M. D. Kovalev

N. E. Bauman Moscow State Technical University

Abstract: The properties of systems of pairwise distances between points thrown into a Euclidean space have been poorly studied to date. These properties are described in terms of a map called the “edge function” (the “rigidity mapping”) and defining the behaviour of actual frameworks of levers and hinges. The simplest non-trivial case is that of rigidity mappings corresponding to plane frameworks (hingers) all fastened hinges of which lie on one straight line. In this paper rigidity mappings are investigated and examples of such straightened hingers with peculiar properties are presented.

DOI: https://doi.org/10.4213/sm827

Full text: PDF file (434 kB)
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English version:
Sbornik: Mathematics, 2004, 195:6, 833–858

Bibliographic databases:

UDC: 514+531.8
MSC: Primary 51K99, 70B15; Secondary 70B10, 53A17
Received: 08.02.2002 and 24.03.2003

Citation: M. D. Kovalev, “Straightened hinged frameworks”, Mat. Sb., 195:6 (2004), 71–98; Sb. Math., 195:6 (2004), 833–858

Citation in format AMSBIB
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\paper Straightened hinged frameworks
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\transl
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\pages 833--858
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. D. Kovalev, “Some properties of rigidity mapping”, J. Math. Sci., 149:1 (2008), 947–955  mathnet  crossref  mathscinet  zmath  elib
    2. Kovalev M., “Hinged Frameworks with Unusual Geometrical Properties”, Proceedings of Eucomes 08, the Second European Conference on Mechanism Science, 2009, 55–60  zmath  isi
    3. M. D. Kovalev, “Napryazhennosvyazannye konstruktsii”, Chebyshevskii sb., 16:3 (2015), 306–321  mathnet  elib
    4. M. D. Kovalev, “The determinant of the stress matrix and restorability of hinged frameworks from self-stresses”, Izv. Math., 80:3 (2016), 500–522  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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