RUDN Journal of Engineering ResearchRUDN Journal of Engineering Research2312-81432312-8151Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)1792510.22363/2312-8143-2017-18-4-518-527Research ArticleORTHOGONAL CURVED COORDINATE SYSTEM AND FORMING THE SURFACES ON TRAPEZIUM-CURVED PLANSIvanovV N<p>Vyacheslav Nikolaevich Ivanov, doctor of technical science, professor of department of architecture and building of Peoples’ friendship university of Russia. Research interests: geometry, forming and methods of design of the thin space constructions of complex forms.</p>i.v.ivn@mail.ruImomnazarovT S<p>Timur Soibnazarovich Imomnazarov, post - graduated student of department of architecture and building of Peoples’ friendship university of Russia. Research interests: construction mechanics, geometry, surface shaping and methods for calculating thin-walled structures of complex shapes.</p>timur-imomnazarov@mail.ruFarhanI T<p>Ismael Taha Farhan, post - graduated student of department of architecture and building of Peoples’ friendship university of Russia. Research interests: construction mechanics, geometry, surface shaping and methods for calculating thin-walled structures of complex shapes.</p>ismael.civilengineer@gmail.comPeoples’ Friendship University of Russia1512201718451852701032018Copyright © 2017, Ivanov V.N., Imomnazarov T.S., Farhan I.T.2017<p>Thin space constructions on curved plans there are used at building of public structures, trade centers. Sport constructions. Working-out the methods of forming of the surfaces on the curved plans that is one of the modern task of the architecture and town building. The orthogonal coordinate system that is formed at the plane with some plane directrix curve and the system of the right lines orthogonal to the directrix curve there is regarded at the stat. The coordinate system forms some trapezium-curved segment. Taking some function of the vertical coordinate there is possible to receive different surfaces at the curved plans. Conjugating different directrix curves, its possible to receive the combined surfaces. The article presents a system of orthogonal coordinates of curvilinear-trapezoidal planes and methods for forming surfaces on these planes. Surfaces with a function of the vertical coordinate of a general view are considered, and surfaces on combined plans of segments of the same type are shown.</p>plane curveorthogonal curved coordinate systemcurved promethium planforming of the surfaces on curved plansплоская криваяортогональная криволинейная система координаткри-волинейно-трапециевидный планформообразование поверхностей на криволинейных пла-нах[Ivanov V.N. Architectural compositions on the base of Coons surfaces. — Structural mechanics of engineering constructions and buildings. 2007. No. 4. P. 5—10.][Ivanov V.N., Romanova V.A. Constructive forms of space constructions. Visualization of the surfaces at the systems “MathCad” and “AUTOCad”: monograph. Moscow: Izd-vo ASV, 2016. 412 p.][Steven А. Coons. Surfaces for Computer-Aided Design in Space Form. Massachusetts Institute of Technology Cambridge, MA, USA, 1967.][Ivanov V.N. Ruled surfaces on the given supporting curves. Structural mechanics of engineering constructions and buildings. 2015. No. 3. P. 9—16.][Ivanov V.N. Geometry and forming of the modified Coons surfaces. Vestnik of Peoples` Friendship University of Russia. Ser.: Engineering investigations. 2011. No. 2. P. 85—90.][Ivanov V.N. The forming of the surfaces on the curved counter planes. Structural mechanics of engineering constructions and buildings. 2017. No. 3. P. 3—8.][Monge G. Memoire sur l’entegrationsde quelques equations aux derives partielles. Mem. Ac. sci. 1787. 309 p.][Ivanov V.N. Geometry of Monge surfaces and construction of the shells. Structural mechanics of engineering constructions and buildings. Mezhvuzovskie sbornic of science works. Vip. 11. Moscow: Izd-vo ASV, 2002. P. 27—36.][Bulca B., Arslan K. (2013) Surfaces Given with the Monge Patch in E. Jour. Math. phis., Analit., Geom. 9(4). P. 435—447.]