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Summary:
The paper presents the deduction of the equations of surfaces between the principal curvatures of which the defined relation is valid. This relation represents the characteristic curvature of the surface.
The differential equation of the surface of characteristic curvature in Cartesian coordinates is deduced in Section 1 for the case that the ratio between the principal curvatures is constant. Some properties of this surface are given in Section 2.
In Section 3 the differential equation of the meridian of a rotary surface of characteristic curvature is deduced. Particular cases of this equation are solved in Section 4.
In Section 5 the author deduces parametric equations of the meridian of the rotary surface using the first integral of differential equation; in Section 6 he demonstrates their practical application to technology.
References:
[1] Eisenhart L. P.: An Introduction to Differential Geometry with Use of the Tensor Calculus. Princeton Univ. Press, Princeton 1947. MR 0003048 | Zbl 0033.01801
[2] Budinský A, Kepr B.: Základy diferenciální geometrie s technickými aplikacemi. (Fundamentals of differential geometry with technical applications). SNTL, Praha 1970.
[3] Hostinský В.: Diferenciální geometrie křivek a ploch. (Differential geometry of curves and surfaces). Přírodovědecké nakladatelství, Praha 1950.
[4] Власов В. 3.: Избранные труды, том 1. Изд. Академии наук СССР, Москва 1962. Zbl 0303.53006
[5] Камке Э.: Справочник по обыкновенным дифференциальным уравнениям. Изд. "Наука", Москва 1971. Zbl 1170.92344
[6] Градштейн И. С., Рыжик И. M.: Таблицы интегралов сумм, рядов и произведений. Физматгиз, Москва 1962. Zbl 1005.68507
[7] Отто Ф., Тростелъ Р.: Пневматические строительные конструкции. Стройиздат Москва 1972. Zbl 1170.01322
[8] Fiřt V.: Vývoj membránových konstrukcí. (Development of membrane structures), Inženýrské stavby 20, 1972, с. 8-9, 321-326.
[9] Fiřt V.: Air-supported structures with automatic adjustment of inner overpressure. Int. Symp. on Pneumatic Structures, Proc., Vol. 2, Delft 1972.
[10] Новожилов В. В.: Теория тонких оболочек. Судпромгиз, Ленинград 1962. Zbl 1005.68507
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