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2011, vol. 3, br. 2, str. 102-115
Šta se nalazi između krutosti i savitljivosti struktura
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria

e-adresastachel@dmg.tuwien.ac.at
Ključne reči: krutost; savitljivost; neograničena savitljivost; savitljivi poliedar; poliedar zategnutuh ivica; kokotsakis mreže; origami mehanizmi
Sažetak
Granična linija između neprekidne savitljivosti i krutosti struktura kao što su poliedar ili ramovske konstrukcije nije striktna. Različiti nivoi bezgranične savitljivosti mogu da postoje. Ovaj članak predstavlja matematičku pozadinu i daje neke primere struktura koje su pod određenim uslovima savitljive ili skoro savitljive, a inače su krute.
Reference
Alexandrov, V. (1998) Sufficient conditions for the extendibility of an n-th order flex of polyhedra. Beitr. Algebra Geom, 39, br. 2, 367-378
Bricard, R. (1897) Memoire sur la theorie de loctaedre articule. J. math. pur. appl., Liouville, 3, 113-148
Cauchy, A.L. (1813) Recherche sur les polyedres: Second memoire. J. Ecole Polytechnique, 9, 87-96
Connelly, R. (1978) A flexible sphere. Mathematical Intelligencer, 1(3): 130-131
Izmestiev, I. (2009) Projective background of the infinitesimal rigidity of frameworks. Geom. Dedicata, 140: 183
Kokotsakis, A. (1932) Über bewegliche Polyeder. Math. Ann, 107, 627-647
Liebmann, H. (1920) Ausnahmefachwerke und ihre Determinante. u: Sb. Bayer. Akad. Wiss, 197-227
Stachel, H. (1999) Infinitesimal flexibility of higher order for a planar parallel manipulator. u: Karane G., Sachs H., Schipp F. [ur.] Topics in algebra, analysis and geometry, BPR Kiado, str. 343-353
Stachel, H. (1999) Higher-order flexibility for a bipartite planar framework. u: Kecskemethy A., Schneider M., Woernle C. [ur.] Advances in multi-body systems and mechatronics, Graz - Duisburg: Inst. F. Mechanik und Getriebelehre, str. 345-357
Stachel, H. (2002) Configuration theorems on bipartite frameworks. Rend. Circ. Mat. Palermo, II, Ser., 70, 335-351
Stachel, H. (2009) Remarks on Miura-ori, a Japanese folding method. Acta Technica Napocensis, Ser. Applied Mathematics and Mechanics, 52, vol. Ia, 245-248
Stachel, H. (to appear) A kinematic approach to Kokotsakis meshes. Comput. Aided Geom. Des
Steffen, K. A symmetric flexible Connelly sphere with only nine vertices. www.math.cornell.edu/~connelly/Steffen.pdf
Velimirović, L.S., Rančić, S.R. (2009) Notes on infinitesimal bending of a toroid formed by revolution of a polygonal meridian. J. Geometry Graphics, 13, br. 2, 177-186
Wegner, B. (1984) On the projective invariance of shaky structures in euclidean space. Acta Mechanica, 53(3-4): 163-171
Whiteley, W. (1984) Infinitesimal motions of a bipartite framework. Pacific J. of Math, 110, 233-255
Whiteley, W. (1997) Rigidity and scene analysis. u: Goodman J.E., O'Rourke J. [ur.] Handbook of discrete and computational geometry, Boca Raton - New York: CRC Press
Wunderlich, W., Schwabe, C. (1986) Eine Familie von geschlossenen gleichfl\'achigen Polyedern, die fast beweglich sind. Elem. Math., 41(4): 88
Wunderlich, W. (1965) Starre, kippende, wackelige und bewegliche Achtflache. Elem. Math, 20, 25-32
 

O članku

jezik rada: engleski
vrsta rada: originalan članak
DOI: 10.5937/SAJ1102102S
objavljen u SCIndeksu: 30.03.2012.

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