Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2421910.22363/2658-4670-2020-28-2-141-153Mathematical models in PhysicsМатематические модели в физикеResearch ArticleKinematic support modeling in SageМоделирование кинематических опор в SageKroytorOleg K.КройторО. К.Postgraduate of Department of Applied Probability and InformaticsКафедра прикладной информатики и теории вероятностейkroytor_ok@pfur.ruMalykhMikhail D.МалыхМ. Д.Doctor of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and InformaticsКафедра прикладной информатики и теории вероятностейmalykh_md@pfur.ruKarnilovichSergei P.КарниловичС. П.assistant professor, Ph.d., assistant professor of Institute of Physical Research and TechnologyИнститут физических исследований и технологийkarnilovich_sp@pfur.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народов15122020282VOL 28, NO2 (2020)ТОМ 28, №2 (2020)14115320072020Copyright ©; 2020, Kroytor O.K., Malykh M.D., Karnilovich S.P.Copyright ©; 2020, Кройтор О.К., Малых М.Д., Карнилович С.П.2020Kroytor O.K., Malykh M.D., Karnilovich S.P.Кройтор О.К., Малых М.Д., Карнилович С.П.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/24219The article discusses the kinematic support, which allows reducing the horizontal dynamic effects on the building during earthquakes. The model of a seismic isolation support is considered from the point of view of classical mechanics, that is, we assume that the support is absolutely solid, oscillating in a vertical plane above a fixed horizontal solid plate. This approach allows a more adequate description of the interaction of the support with the soil and the base plate of the building. The paper describes the procedure for reducing the complete system of equations of motion of a massive rigid body on a fixed horizontal perfectly smooth plane to a form suitable for applying the finite difference method and its implementation in the Sage computer algebra system. The numerical calculations by the Euler method for grids with different number of elements are carried out and a mathematical model of the support as a perfectly rigid body in the Sage computer algebra system is implemented. The article presents the intermediate results of numerical experiments performed in Sage and gives a brief analysis (description) of the results.В статье рассмотрена кинематическая опора, которая позволяет снижать горизонтальные динамические воздействия на здание во время землетрясений. Модель сейсмоизолирующей опоры рассматривается с точки зрения классической механики, то есть предполагается, что опора - абсолютно твёрдое тело, колеблющееся в вертикальной плоскости над неподвижной горизонтальной твёрдой плитой. Данный подход позволяет более адекватно описать взаимодействие опоры с грунтом и плитой здания. В работе описана процедура сведения полной системы уравнений движения тяжёлого твёрдого тела по неподвижной горизонтальной абсолютно гладкой плоскости к виду, пригодному для применения метода конечных разностей, и её реализация в системе компьютерной алгебры Sage. Проведены численные расчёты методом Эйлера для сеток с разным количеством разбиений и реализована математической модель опоры как абсолютно твёрдого тела в системе компьютерной алгебры Sage. В статье представлены промежуточные результаты численных экспериментов, полученных в Sage, и дан краткий анализ (описание) результатов.kinematic supportseismic isolation supportmathematical modelfinite difference methodcomputer algebra systemSagenumerical calculationsSageкинематическая опорасейсмоизолирующая опораматематическая модельМКРсистема компьютерной алгебрычисленные расчёты1.A. Kurzanov and N. Skladnev, “Seismo-isolating supports for dwellings,” in Earthquake Engineering, Tenth World Conference, Balkema, Rotterdam, 1992, pp. 1951-1954.2.A. M. Kurzanov and S. Y. Semenov. (2013). “Pipe-concrete seismic isolating support [Trubobetonnaya seysmoizoliruyuschaya opora],” [Online]. Available: https://patents.google.com/patent/RU2477353C1/enl.3.Y. Cherepinsky, “Seismic stability of buildings on kinematic supports,” Soil Mech Found Eng, vol. 9, pp. 164-168, 1972. DOI: 10.1007/ BF01709306.4.Y. Cherepinsky, “The seismic isolation of residential buildings,” Res. Seism. Stab. Build. 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