Algorithms for compiling a mathematical model of physical systems using graphs
DOI:
https://doi.org/10.21638/11701/spbu10.2024.102Abstract
A system of algorithms for compiling a mathematical model of physical systems, the structure of which is given using graphs of great complexity, is proposed. The proposed algorithms can be used not only to develop new systems, but also to diagnose operating equipment and troubleshooting. The resulting mathematical model of the system, presented in the form of a system of equations, allows us to obtain a unique solution. The operation of the algorithms is illustrated using the example of a mechanical system, but the results of the work can be extended to systems of a different nature using electromechanical or electroeconomic analogies.
Keywords:
graph, graph connectivity, fundamental cycle
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Нечепуренко М. И., Попков В. К., Майнагашев С. М. Алгоpитмы и пpогpаммы pешения задач на гpафах и сетях. Hовосибиpск: Hаука, 1990. 520 с.
Седжвик Р. Фундаментальные алгоритмы на C++ / пер. с англ. А. А. Моргунова; под ред. Ю. Н. Артеменко. М.: Вильямс, 2016. 1056 с.
Новиков Ф. А. Дискретная математика для программистов. СПб.: Питер, 2004. 368 с.
Курапов С. В., Давидовский М. В. Проверка планарности и построение топологического рисунка плоского графа (поиском в глубину) // Прикладная дискретная математика. 2016. № 2 (32). С. 100–114. https://doi.org/10.17223/20710410/32/7
Свами М., Тхуласираман К. Графы, сети и алгоритмы / пер. с англ. М. В. Горбатовой и др.; под ред. В. А. Горбатова. М.: Мир, 1984. 455 с.
Львович А. Ю. Электромеханические системы. Л.: Изд-во Ленинградского государственного университета, 1989. 296 с.
Карпов А. Г., Клемешев В. А., Куранов Д. Ю. Определение работоспособности системы, структура которой задана графом // Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления. 2020. Т. 16. Вып. 1. С. 41–49. https://doi.org/10.21638/11702/spbu10.2020.104.
References
Nechepurenko M. I., Popkov V. K., Mainagashev S. M. Algoritmy i programmy resheniya zadach na grafah i setyah [Algorithms and programs for solving problems on graphs and networks]. Novosibirsk, Nauka Publ., 1990, 520 p. (In Russian)
Sedgewick R. textit Algorithms in C++. Boston, Addison-Wesley Professional, 2009, 672 p. (Rus. ed.: Sedgewick R. textit Algoritmy na C++. Moscow, Williams Publ., 2016, 1056 p.)
Novikov F. A. Diskretnaya matematika dlya programmistov [Discrete mathematics for programmers]. St. Petersburg, Piter Publ., 2004, 368 p. (In Russian)
Kurapov S. V., Davidovsky M. V. Proverka planarnosti i postroenie topologicheskogo risunka ploskogo grafa (poiskom v glubinu) [Planarity testing and constructing the topological drawing of a plane graph (DFS)]. Prikladnaya Diskretnaya Matematika [Applied Discrete Mathematics], 2016, no. 2 (32), pp. 100–114. https://doi.org/10.17223/20710410/32/7 (In Russian)
Swamy M. N. S., Thulasiraman K. textit Graphs, networks, and algorithms. New York, Wiley-Interscience, 1981, 592 p. (Rus. ed.: Swamy M., Thulasiraman K. textit Grafy, seti i algoritmy. Moscow, Mir Publ., 1984, 455 p.)
L’vovich A. Yu. Elektromehanicheskie sistemy [Electromechanical systems]. Leningrad, Leningrad State University Press, 1989, 296 p. (In Russian)
Karpov A. G., Klemeshev V. A., Kuranov D. Yu. Opredelenie rabotosposobnosti systemy, struktura kotoroy zadana grafom [Determining the ability to work of the system, the structure of which is given using graph]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 1, pp. 41–49. https://doi.org/10.21638/11702/spbu10.2020.104 (In Russian)
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Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
