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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">novtexmech</journal-id><journal-title-group><journal-title xml:lang="ru">Мехатроника, автоматизация, управление</journal-title><trans-title-group xml:lang="en"><trans-title>Mekhatronika, Avtomatizatsiya, Upravlenie</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1684-6427</issn><issn pub-type="epub">2619-1253</issn><publisher><publisher-name>Commercial Publisher «New Technologies»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17587/mau.26.316-325</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-1773</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ДИНАМИКА, БАЛЛИСТИКА, УПРАВЛЕНИЕ ДВИЖЕНИЕМ ЛЕТАТЕЛЬНЫХ АППАРАТОВ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>DYNAMICS, BALLISTICS AND CONTROL OF AIRCRAFT</subject></subj-group></article-categories><title-group><article-title>Поиск нестационарного объекта роевой системой мультикоптеров на основе метода квазитеплового движения</article-title><trans-title-group xml:lang="en"><trans-title>Search of Non-Stationary Object by Multicopter Swarm Based on Thermal Motion Equivalent Method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гейс</surname><given-names>Э. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Heiss</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мл. науч. сотр. </p><p>Тула</p></bio><bio xml:lang="en"><p>Postgraduate Student </p><p>Tula, 300012 </p></bio><email xlink:type="simple">edheiss73@outlook.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Козырь</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kozyr</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Канд. тех. наук, ст. науч. сотр.</p><p>Тула</p></bio><bio xml:lang="en"><p>Tula, 300012 </p></bio><email xlink:type="simple">Kozyr_A_V@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Морозов</surname><given-names>О. О.</given-names></name><name name-style="western" xml:lang="en"><surname>Morozov</surname><given-names>O. O.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Канд. тех. наук, доц. </p><p>Тула</p></bio><bio xml:lang="en"><p>Tula, 300012 </p></bio><email xlink:type="simple">omo@sau.tsu.tula.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБОУ ВО "Тульский государственный университет"</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tula State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>05</day><month>06</month><year>2025</year></pub-date><volume>26</volume><issue>6</issue><fpage>316</fpage><lpage>325</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Commercial Publisher «New Technologies»</copyright-holder><copyright-holder xml:lang="en">Commercial Publisher «New Technologies»</copyright-holder><license xlink:href="https://mech.novtex.ru/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://mech.novtex.ru/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://mech.novtex.ru/jour/article/view/1773">https://mech.novtex.ru/jour/article/view/1773</self-uri><abstract><p>Решается задача поиска нестационарного объекта в ограниченной топологически замкнутой области многоагентной системой летательных аппаратов квадрокоптерного типа. В качестве алгоритма управления многоагентной системой предлагается метод квазитеплого движения (МКТД). Идейно МКТД основан на поведенческом повторении движения частиц газа, где с помощью уже известных из термодинамики интегральных параметров, таких как среднеквадратичная скорость, частота взаимодействий, оценивается устойчивость системы и качество решения поставленных перед роем задач. Условная аналогия движений летательных аппаратов с молекулярной динамикой в МКТД обеспечивается системой управления каждого агента, которые могут информационно взаимодействовать друг с другом. В работе показана эффективность применения метода МКТД к поиску динамической цели в ограниченном пространстве на основе многочисленных моделирований в специально разработанной среде MASPlatform, представляющей виртуальный полигон. В программном обеспечении MASPlatform реализовано движение тридцати агентов в пространстве размером 300 на 300 м. Динамика каждого агента описана системой нелинейных дифференциальных уравнений с кватернионным регулятором. На основе многочисленных моделирований поисковой задачи МКТД делается вывод об эффективности.Получены оценки численности роя в зависимости от пространства поиска. Предложен подход к оценке времени поиска роевой системой, функционирующей в режиме МКТД, нестационарного объекта с известной динамикой в ограниченном пространстве на основе термодинамического параметра "средняя длина свободного пробега". Данный параметр важен для реальных систем, где есть ограничения энергетического ресурса агента.</p></abstract><trans-abstract xml:lang="en"><p>The paper presents the issue result of searching a non-stationary object in a topologically closed bounded area by a multi-agent system of quadrocopter-type aircraft. Thermal motion equivalent method (TMEM) method is proposed as a control algorithm for the multi-agent system. The TMEM is based on the similarity of the motion of molecules. In the case of TMEM it is possible to estimate swarm stability and performance of swarm problem solving using integral parameters already known from thermodynamics: RMS velocity, frequency of interactions and others. The aircraft motion similar to a molecular dynamic in TMEM is provided by the control system of each agent interacted with others by data exchanging. The paper demonstrates the effectiveness of applying the TMEM method to the search for a dynamic target in a bounded area based on numerous simulations in a specially designed MASPlatform environment representing a virtual polygon. The MASPlatform software implements the motion of thirty agents in a space of 300 by 300 meters. The dynamics of each agent is represented by a system of nonlinear differential equations with a quaternionic controller. The inference of efficiency is made based on multiple simulations of the ICD search issue.In this paper, estimates of swarm numbers as a function of the search space are obtained. The paper proposes an approach to estimating the search time of a non-stationary object with known dynamics by a swarm, whose agents interact using TMEM in a bounded area, based on the thermodynamic parameter "mean free path length". This parameter is important for real systems where there are constraints on the agent’s energy resource.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>групповое управление</kwd><kwd>рой ЛА</kwd><kwd>метод квазитеплового движения</kwd><kwd>поиск группой агентов</kwd><kwd>многоагентное управление</kwd></kwd-group><kwd-group xml:lang="en"><kwd>swarm control</kwd><kwd>swarm UAV</kwd><kwd>thermal motion equivalent method (TMEM)</kwd><kwd>search by a group of agents</kwd><kwd>multi-agent control</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда № 23-29-10077, https://rscf.ru/project/23-29-10077/</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Savkin A. V., Huang H. Multi-UAV Navigation for Optimized Video Surveillance of Ground Vehicles on Uneven Terrains // IEEE Transactions on Intelligent Transportation Systems. Sept. 2023. Vol. 24, N. 9. P. 10238—10242. DOI: 10.1109/TITS.2023.3270969.</mixed-citation><mixed-citation xml:lang="en">Savkin A. V., Huang H. Multi-UAV Navigation for Optimized Video Surveillance of Ground Vehicles on Uneven Terrains, IEEE Transactions on Intelligent Transportation Systems, 2023, vol. 24, no. 9, pp. 10238—10242, doi: 10.1109/TITS.2023.3270969.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Li X., Yang L. Design and Implementation of UAV Intelligent Aerial Photography System // 2012 4th International Conference on Intelligent Human-Machine Systems and Cybernetics. Nanchang, China, 2012. P. 200—203. DOI: 10.1109/IHMSC.2012.144.</mixed-citation><mixed-citation xml:lang="en">Li X., Yang L. Design and Implementation of UAV Intelligent Aerial Photography System, 2012 4th International Conference on Intelligent Human-Machine Systems and Cybernetics, Nanchang, China, 2012, pp. 200—203, doi: 10.1109/IHMSC.2012.144.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Betti Sorbelli F. UAV-Based Delivery Systems: A Systematic Review, Current Trends, and Research Challenges // ACM Journal on Autonomous Transportation Systems. 2024. DOI: 10.1145/3649224.</mixed-citation><mixed-citation xml:lang="en">Betti Sorbelli F. UAV-Based Delivery Systems: A Systematic Review, Current Trends, and Research Challenges. ACM Journal on Autonomous Transportation Systems, 2024, doi: 10.1145/3649224.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Golam M., Akter R., Tuli E. A., Kim D.-S., Lee J.-M. Lightweight Blockchain Assisted Unauthorized UAV Access Prevention in the Internet of Military Things // 2022 13th International Conference on Information and Communication Technology Convergence (ICTC). Jeju Island, Korea, Republic of. 2022. P. 890—894. DOI: 10.1109/ICTC55196.2022.9953024.</mixed-citation><mixed-citation xml:lang="en">Golam M., Akter R., Tuli E. A., Kim D.-S., Lee J. -M. Lightweight Blockchain Assisted Unauthorized UAV Access Prevention in the Internet of Military Things, 2022 13th International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Korea, Republic of, 2022, pp. 890—894, doi: 10.1109/ICTC55196.2022.9953024.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Филимонов А. Б., Филимонов Н. Б., Нгуен Т. К., Фам К. Ф. Оптимизация маршрутов полета БПЛА при групповом патрулировании протяженных территорий как множественная задача коммивояжера с несколькими депо // Мехатроника, автоматизация, управление. 2024. Vol. 25, N. 5. P. 259—265. URL: https://doi.org/10.17587/mau.25.259-265.</mixed-citation><mixed-citation xml:lang="en">Filimonov A. B., Filimonov N. B., Nguyen Т. К., Pham Q. P. Optimization of UAV Flight Routes during Group Patrolling of Extended Territories as a Multiple Task of a Traveling Salesman with Several Depots, Mekhatronika, Avtomatizatsiya, Upravlenie. 2024, vol. 25, no. 5, pp. 259—265 (In Russ.), doi: 10.17587/mau.25.259-265.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Wood J., Hedrick J. Space Partitioning and Classification for Multi-target Search and Tracking by Heterogeneous Unmanned Aerial System Teams // AIAA Infotech at Aerospace Conference and Exhibit. 2011. DOI: 10.2514/6.2011-1443.</mixed-citation><mixed-citation xml:lang="en">Wood J., Hedrick J. Space Partitioning and Classification for Multi-target Search and Tracking by Heterogeneous Unmanned Aerial System Teams, AIAA Infotech at Aerospace Conference and Exhibit, 2011, doi: 10.2514/6.2011-1443.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Liu X., Liu Y., Chen Y. Reinforcement Learning in Multiple-UAV Networks: Deployment and Movement Design // IEEE Transactions on Vehicular Technology. 2019. P. 1-1. DOI: 10.1109/TVT.2019.2922849.</mixed-citation><mixed-citation xml:lang="en">Liu X., Liu Y., Chen Y. Reinforcement Learning in MultipleUAV Networks: Deployment and Movement Design, IEEE Transactions on Vehicular Technology, pp. 1-1, doi: 10.1109/TVT.2019.2922849.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Z., Gao X., Fu X. A Cooperative Search and Coverage Algorithm with Controllable Revisit and Connectivity Maintenance for Multiple Unmanned Aerial Vehicles // Sensors. 2018. Т. 18, № 5.</mixed-citation><mixed-citation xml:lang="en">Liu Z., Gao X., Fu X. A Cooperative Search and Coverage Algorithm with Controllable Revisit and Connectivity Maintenance for Multiple Unmanned Aerial Vehicles, Sensors, 2018, vol. 18, no. 5.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Pyke L., Stark C. Dynamic Pathfinding for a Swarm Intelligence Based UAV Control Model Using Particle Swarm Optimisation // Frontiers in Applied Mathematics and Statistics. 2021. N. 7. DOI: 10.3389/fams.2021.744955.</mixed-citation><mixed-citation xml:lang="en">Pyke L., Stark C. Dynamic Pathfinding for a Swarm Intelligence Based UAV Control Model Using Particle Swarm Optimisation, Frontiers in Applied Mathematics and Statistics, 2021, no. 7, doi: 10.3389/fams.2021.744955.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">He Y., Zeng Q., Liu J., Xu G., Xiaoyi D. Path planning for indoor UAV based on Ant Colony Optimization // 25th Chinese Control and Decision Conference, CCDC. 2013. P. 2919—2923. DOI: 10.1109/CCDC.2013.6561444.</mixed-citation><mixed-citation xml:lang="en">He Y., Zeng Q., Liu J., Xu G., Xiaoyi D. Path planning for indoor UAV based on Ant Colony Optimization. 25th Chinese Control and Decision Conference, CCDC, 2013, pp. 2919—2923, doi: 10.1109/CCDC.2013.6561444.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Bolaji A., Khader A. T., Al-Betar M., Awadallah M. Artificial bee colony algorithm, its variants and applications: A survey // Journal of Theoretical and Applied Information Technology. 2013. N. 47. P. 434—459.</mixed-citation><mixed-citation xml:lang="en">Bolaji A., Khader A. T., Al-Betar M., Awadallah M. Artificial bee colony algorithm, its variants and applications: A survey. Journal of Theoretical and Applied Information Technology, 2013, no. 47, pp. 434—459.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Гейс Э. А., Морозов О. О., Козырь А. В., Ефромеев А. Г. Методика синтеза регулятора мультикоптера, функционирующего в качестве агента роевой системы по методу квазитеплового движения // Мехатроника, автоматизация, управление. 2024. Т. 25, № 1. С. 43—52. DOI: 10.17587/mau.25.43-52.</mixed-citation><mixed-citation xml:lang="en">Heiss E. A., Morozov O. O., Kozyr A. V., Efromeev A. G. Methodology for the Synthesis of a Multicopter Controller Acting as a Swarm Agent using the Thermal Motion Equivalent Method, Mekhatronika, Avtomatizatsiya, Upravlenie, 2024, vol. 25, no. 1, pp. 43—52 (in Russian), doi: 10.17587/mau.25.43-52.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Heiss E., Kozyr A., Morozov O. Synchronization of the Coupled Swarm Agents’ Movement Interacting by the Thermal Motion Equivalent Method // International Conference of Young Specialists on Micro/Nanotechnologies and Electron Devices. EDM. 2024. P. 1600—1607.</mixed-citation><mixed-citation xml:lang="en">Heiss E., Kozyr A., Morozov O. Synchronization of the Coupled Swarm Agents’ Movement Interacting by the Thermal Motion Equivalent Method, International Conference of Young Specialists on Micro/Nanotechnologies and Electron Devices, EDM, 2024, pp. 1600—1607.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Heiss E., Kozyr A., Morozov O. Interaction Between Area Boundary and Formation of Agents Interacting by the Thermal Motion Equivalent Method // Proceedings — 2024 International Conference on Industrial Engineering, Applications and Manufacturing. ICIEAM 2024. 2024. P. 771—777.</mixed-citation><mixed-citation xml:lang="en">Heiss E., Kozyr A., Morozov O. Interaction Between Area Boundary and Formation of Agents Interacting by the Thermal Motion Equivalent Method, Proceedings — 2024 International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2024, 2024, pp. 771—777.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Heiss E., Morozov O., Efromeev A. Assessing the similarity of atoms’ thermal motion behavior by swarm agents // 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA). Lipetsk. IEEE, 2022. P. 92—96.</mixed-citation><mixed-citation xml:lang="en">Heiss, E., Morozov O., Efromeev A. Assessing the similarity of atoms’ thermal motion behavior by swarm agents. 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, IEEE, 2022, pp. 92—96.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Bansal S., Goel R., Maini R. Ground Vehicle and UAV Collaborative Routing and Scheduling for Humanitarian logistics using Random Walk Based Ant Colony Optimization // Scientia Iranica. 2022. Vol. 29, N. 2. P. 632—644.</mixed-citation><mixed-citation xml:lang="en">Bansal S., Goel R., Maini R. Ground Vehicle and UAV Collaborative Routing and Scheduling for Humanitarian logistics using Random Walk Based Ant Colony Optimization, Scientia Iranica, 2022, vol. 29, no. 2, pp. 632—644.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Z., Qiu C., Zhang Z. Sequence-to-Sequence MultiAgent Reinforcement Learning for Multi-UAV Task Planning in 3D Dynamic Environment // Applied Sciences. 2022. N. 12. P. 12181. 10.3390/app122312181.</mixed-citation><mixed-citation xml:lang="en">Liu Z., Qiu C., Zhang Z. Sequence-to-Sequence MultiAgent Reinforcement Learning for Multi-UAV Task Planning in 3D Dynamic Environment. Applied Sciences, 2022, no. 12, pp. 12181, doi: 10.3390/app122312181.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Костюков В. А., Медведев М. Ю., Пшихопов В. Х. Планирование движения наземных роботов в среде с препятствиями: алгоритмы построения траекторий в группе при заданном шаблоне // Мехатроника, автоматизация, управление. 2023. Т. 24, № 1. С. 33—45. DOI: 10.17587/mau.24.33-45.</mixed-citation><mixed-citation xml:lang="en">Kostjukov V. A., Medvedev M. Y., Pshikhopov V. Kh. Algorithms for Path Planning in a Group of Mobile Robots in an Environment with Obstacles with a Given Template, Mekhatronika, Avtomatizatsiya, Upravlenie, 2023, vol. 24, no. 1, pp. 33—45 (in Russian), doi: 10.17587/mau.24.33-45.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Jing Y. Research on Multi-UAV Swarm Control Based on Olfati-Saber Algorithm with Variable Speed Virtual Leader // IoT as a Service. Cham: Springer International Publishing, 2021. P. 14—22.</mixed-citation><mixed-citation xml:lang="en">Jing Y. Research on Multi-UAV Swarm Control Based on Olfati-Saber Algorithm with Variable Speed Virtual Leader, IoT as a Service, Cham: Springer International Publishing, 2021, pp. 14—22.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Sho R., Tao R., Liu Y., Yang Y., Li D., Chen J. UAV cooperative search in dynamic environment based on hybrid-layered APF // EURASIP Journal on Advances in Signal Processing. 2021. Vol. 2021, N. 1. P. 101.</mixed-citation><mixed-citation xml:lang="en">Sh o R., Tao R., Liu Y., Yang Y., Li D., Chen J. UAV cooperative search in dynamic environment based on hybrid-layered APF, EURASIP Journal on Advances in Signal Processing, 2021, vol. 2021, no. 1, pp. 101.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Sutantyo D., Kernbach S., Nepomnyashchikh V., Levi P. Multi-Robot Searching Algorithm Using Levy Flight and Artificial Potential Field // 2010 8th IEEE International Workshop on Safety, Security, and Rescue Robotics. Bremen, Germany. 2011. P. 1—6.</mixed-citation><mixed-citation xml:lang="en">Sutantyo D., Kernbach S., Nepomnyashchikh V., Levi P. Multi-Robot Searching Algorithm Using Levy Flight and Artificial Potential Field, 2010 8th IEEE International Workshop on Safety, Security, and Rescue Robotics, Bremen, Germany, 2011, pp. 1—6.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Филимонов А. Б., Филимонов Н. Б. The Concept of Fairway in Problems of Potential Guidance of Mobile Robots // Optoelectronics, Instrumentation and Data Processing. 2022. Vol. 58, № 4. С. 366—372.</mixed-citation><mixed-citation xml:lang="en">Filimonov A. B., Filimonov N. B. The Concept of Fairway in Problems of Potential Guidance of Mobile Robots, Optoelectronics, Instrumentation and Data Processing, 2022, vol. 58, pp. 366—372, doi: 10.3103/S8756699022040057.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Евдокимов И. Н., Елисеев Н. Ю. Молекулярные механизмы вязкости жидкости и газа. Часть 1. Основные понятия. М.: Изд. Российский государственный университет нефти и газа имени И. М. Губкина, 2005. 59 с.</mixed-citation><mixed-citation xml:lang="en">Evdokimov I. N., Eliseev N. Yu. Molecular mechanisms of viscosity of liquid and gas. Part 1. Basic concepts, Moscow, Gubkin Russian State University of Oil and Gas, 2005, 59 p.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Сивухин Д. В. Общий курс физики. Термодинамика и молекулярная физика. Т. 2. М.: ФИЗМАТЛИТ, 2021. 544 с.</mixed-citation><mixed-citation xml:lang="en">Sivukhin D. V. General course of physics. Thermodynamics and molecular physics, vol. 2, Moscow, PHYSMATLIT, 2021, 544 с.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
