Geodesic
To the question on continuous parameterization of spatial figures having an ellipse in a section
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 30-35.

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In solving problems of mechanics of shells by numerical methods, inevitably arises a problem of continuous parameterization of calculated shell construction, requiring a calculation of necessary geometrical descriptions in an arbitrary point of examined shell. At that, position of a point must be completely defined, and the used geometrical parameters must have clear geometrical interpretation. We propose new variants of formulas, allowing to execute continuous parameterization of spatial figures having an ellipse in a section, and possessing clear geometric interpretation.
Keywords: radius-vector, parameterization of spatial figures, ellipse. 
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Yu. V. Klochkov; A. P. Nikolaev; T. A. Kiseleva. To the question on continuous parameterization of spatial figures having an ellipse in a section. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 30-35. http://geodesic.mathdoc.fr/item/IVM_2017_9_a2/

[1] Pogorelov A.V., Differentsialnaya geometriya, Nauka, M., 1974

[2] Borisenko A.I., Tarapov I.E., Vektornyi analiz i nachala tenzornogo ischisleniya, Vyssh. shkola, M., 1966

[3] Novozhilov V.V., Teoriya tonkikh obolochek, Izd-vo S.-Peterb. un-ta, SPb., 2010

[4] Sedov L.I., Mekhanika sploshnoi sredy, Nauka, M., 1976

[5] Golovanov A.I., Tyuleneva O.N., Shigabutdinov A.F., Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsii, Fizmatlit, M., 2006

[6] Skopinskii V.N., Napryazheniya v peresekayuschikhsya obolochkakh, Fizmatlit, M., 2008

[7] Bathe K.J., Finite element procedures, Prentice Hall, N.J., 1996

[8] Oden Dzh., Konechnye elementy v nelineinoi mekhanike sploshnykh sred, Mir, M., 1976

[9] Krivoshapko S.N., Ivanov V.N., Encyclopedia of Analytical Surfaces, Springer, International Publishing, Switzeland, 2015 | MR | Zbl

[10] Aleksandrov P.S., Lektsii po analiticheskoi geometrii, popolnennye neobkhodimymi svedeniyami iz algebry s prilozheniem sobraniya zadach, snabzhennykh resheniyami, sostavlennogo A.S. Parkhomenko, Nauka, M., 1968