Encyclopedia of Analytical Surfaces by S.N. Krivoshapko, V.N. Ivanov

By S.N. Krivoshapko, V.N. Ivanov

This encyclopedia provides an all-embracing selection of analytical floor periods. It presents concise definitions and outline for greater than 500 surfaces and categorizes them in 38 sessions of analytical surfaces. All periods are go references to the unique literature in an exceptional bibliography.
The encyclopedia is of specific curiosity to structural and civil engineers and serves as worthwhile reference for mathematicians.

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By S.N. Krivoshapko, V.N. Ivanov

This encyclopedia provides an all-embracing selection of analytical floor periods. It presents concise definitions and outline for greater than 500 surfaces and categorizes them in 38 sessions of analytical surfaces. All periods are go references to the unique literature in an exceptional bibliography.
The encyclopedia is of specific curiosity to structural and civil engineers and serves as worthwhile reference for mathematicians.

Show description

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In practice, ruled surfaces are of value in avant-garde architecture. Additional Literature Zeyliger DN. Complex Ruled Geometry. Surfaces and Congruencies. , 1934. Rekach VG, Krivoshapko SN. An Analysis of shell of Complex Geometry. Moscow: Izd-vo UDN, 1988; 176 p. , Obuhova VS. The forming of shells from fragments of oblique and developable surfaces of the highest orders. In: Shells in Architecture and Strength Analysis of Thin-Walled Civil-Engineering and Machine-Building Constructions of Complex Forms, Moscow, June 4-8, 2001, Moscow: Izd-vo RUDN, 2001; p.

Grafika. 1979; 27, p. 15-17. ■ Torse with Two Parabolas with Intersecting Axes B(-d; l ) O This developable surface contains two parabolas of the second order as the directrixes (Fig. 1): cos u1 2 z ; 2p1 sin u1 2 z y ¼ F1 ðzÞ ¼ 2p1 cos u2 2 II: x ¼ f2 ðzÞ ¼ z À d; 2p2 sin u2 2 z : y ¼ F2 ðzÞ ¼ l À 2p2 C Fig. 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 b 2 þ þ b; b2 4 2 Parametrical equations of the cuspidal edge of the presented developable surface are x¼ b2 c2 ðsin u1 þ sin u2 Þ À 2yðp1 cos u2 c2 À p2 b2 c0 cos u1 Þ ; 2p1 c2 sin u2 þ 2p2 b2 c0 sin u1 2p1 c3 þ b3 sin u1 ð2c02 À cc00 Þp2 ; 2p1 p2 ð2bc02 À 2cc0 À cbc00 Þ b p2 sin u1 ðx À ctgu1 yÞ p1 sin u2 ðx þ ctgu2 yÞ þ : z¼ þ 2 c sinðu1 þ u2 Þ b sinðu1 þ u2 Þ y¼ u2 À d sin u2 Þ u1 þ d sin u1 Þ ; b ¼ a À 2p2 ðl cos : where a ¼ p1 ðl cos sinðu þu Þ sinðu þu Þ 1 ϕ2 x The axes of the parabolas are intersecting in the point C (Fig.

3) Parametrical equations (Figs. 2 and 3): 0 a 2p; À1 u 1; Fig. 3 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 À r 2 cos2 a x ¼ xðu; aÞ ¼ r cos a À u sin a ; R2 À r 2 cos4 a rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 À r 2 cos2 a y ¼ yðu; aÞ ¼ r sin a þ u cos a ; R2 À r 2 cos4 a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ÃÀ1=2 =2; z ¼ zðu; aÞ ¼ R2 À r 2 cos2 a þ ur sin 2a R2 À r2 cos4 a Reference Voronina AN. Construction of torses with the cuspidal edge in the form of the fourth order curve. Prikl. Geom. i Ingen. Grafika. 1967; 5, p.

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