Straightened hinged frameworks
Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 833-858 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
@article{SM_2004_195_6_a3,
     author = {M. D. Kovalev},
     title = {Straightened hinged frameworks},
     journal = {Sbornik. Mathematics},
     pages = {833--858},
     year = {2004},
     volume = {195},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_6_a3/}
}
TY  - JOUR
AU  - M. D. Kovalev
TI  - Straightened hinged frameworks
JO  - Sbornik. Mathematics
PY  - 2004
SP  - 833
EP  - 858
VL  - 195
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_2004_195_6_a3/
LA  - en
ID  - SM_2004_195_6_a3
ER  - 
%0 Journal Article
%A M. D. Kovalev
%T Straightened hinged frameworks
%J Sbornik. Mathematics
%D 2004
%P 833-858
%V 195
%N 6
%U http://geodesic.mathdoc.fr/item/SM_2004_195_6_a3/
%G en
%F SM_2004_195_6_a3
M. D. Kovalev. Straightened hinged frameworks. Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 833-858. http://geodesic.mathdoc.fr/item/SM_2004_195_6_a3/

[1] Connelly R., “Rigidity”, Handbook of convex geometry, A, eds. P. Gruber et al., North-Holland, Amsterdam, 1993, 223–271 | MR | Zbl

[2] White N., Whiteley W., “The algebraic geometry of stresses in frameworks”, SIAM J. Algebraic Discrete Methods, 4:4 (1983), 481–511 | DOI | MR | Zbl

[3] Kovalev M. D., “Ustoichivost sharnirnikov, sharnirnykh ustroistv i skhem”, Trudy mezhdunarodnoi konferentsii, posvyaschennoi 90-letiyu so dnya rozhdeniya L. S. Pontryagina, Itogi nauki i tekhniki. Sovr. matem. i ee prilozh., 68, VINITI, M., 1999, 65–86 | MR

[4] Kovalev M. D., “Geometricheskaya teoriya sharnirnykh ustroistv”, Izv. RAN. Ser. matem., 58:1 (1994), 45–70 | Zbl

[5] Kovalev M. D., “Kvadratichnye i rychazhnye otobrazheniya”, Diskretnaya geometriya, geometriya chisel i prilozheniya, Trudy MIAN, 239, 2002, 195–214 | MR | Zbl

[6] Agrachev A. A., Gamkrelidze R. V., “Kvadratichnye otobrazheniya i gladkie funktsii: eilerovy kharakteristiki mnozhestv urovnya”, Itogi nauki i tekhniki. Sovr. problemy matem., 35, VINITI, M., 1989, 179–239 | MR

[7] Kovalev M. D., “O vosstanovimosti sharnirnikov po vnutrennim napryazheniyam”, Izv. RAN. Ser. matem., 61:4 (1997), 37–66 | MR | Zbl

[8] Berzhe M., Geometriya, t. 1, Mir, M., 1984 | MR

[9] Dubrovin V. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[10] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, Nauka, M., 1982 | MR

[11] Kovalev M., “Local properties of the rigidity mapping”, Convex and discrete geometry. Abstracts. Bydgoszcz, Institut Matematyki i Fizyki ATR, Poland, 1998, 40

[12] Shafarevich I. R., Osnovy algebraicheskoi geometrii, t. 1, Nauka, M., 1988 | MR

[13] Fulton U., Teoriya peresechenii, Mir, M., 1989 | MR