<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">sibadi</journal-id><journal-title-group><journal-title xml:lang="ru">Научный рецензируемый журнал "Вестник СибАДИ"</journal-title><trans-title-group xml:lang="en"><trans-title>The Russian Automobile and Highway Industry Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2071-7296</issn><issn pub-type="epub">2658-5626</issn><publisher><publisher-name>The Siberian State Automobile and Highway University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26518/2071-7296-2026-23-4-554-566</article-id><article-id custom-type="edn" pub-id-type="custom">IZIUXI</article-id><article-id custom-type="elpub" pub-id-type="custom">sibadi-2311</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>ТРАНСПОРТНОЕ, ГОРНОЕ И СТРОИТЕЛЬНОЕ МАШИНОСТРОЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TRANSPORT, MINING AND BUILDING MACHINERY ENGINEERING</subject></subj-group></article-categories><title-group><article-title>Экспериментальная валидация физически обоснованной математической модели качения колесного движителя по твердой опорной поверхности при прямолинейном движении</article-title><trans-title-group xml:lang="en"><trans-title>Experimental validation of a physically based mathematical model of wheel rolling motion on a solid supporting surface during rectilinear driving</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8851-959X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Жилейкин</surname><given-names>М. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhileykin</surname><given-names>M. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Жилейкин Михаил Михайлович - д-р техн. наук, проф., старший научный сотрудник</p><p>107023, г. Москва, ул. Б. Семёновская, д. 38</p><p>Scopus ID: 57201085829</p></bio><bio xml:lang="en"><p>Zhileykin Mikhail Mikhailovich - Doctor of Technical Sciences, Professor, Senior Research Associate</p><p>38, B. Semyonovskaya St., Moscow, 107023</p><p>Scopus ID: 57201085829</p></bio><email xlink:type="simple">jileykin_m@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0009-4163-3721</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Козелков</surname><given-names>О. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kozelkov</surname><given-names>O. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Козелков Олег Александрович - д-р техн. наук, проф., начальник научно-технического центра «Автоматизированные технические системы» Московского политехнического университета</p><p>107023, г. Москва, ул. Б. Семёновская, д. 38</p></bio><bio xml:lang="en"><p>Kozelkov Oleg Aleksandrovich - Doctor of Technical Sciences, Professor, Head of Scientific and Technical Center “Automated Technical Systems”, Moscow Polytechnic University</p><p>38, B. Semyonovskaya St., Moscow, 107023</p></bio><email xlink:type="simple">kozelkow@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>Косенков</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kosenkov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Косенков Алексей Александрович - аспирант, эксперт</p><p>107023, г. Москва, ул. Б. Семёновская, д. 38</p></bio><bio xml:lang="en"><p>Kosenkov Aleksey Aleksandrovich - postgraduate student, expert</p><p>38, B. Semyonovskaya St., Moscow, 107023</p></bio><email xlink:type="simple">kosenkovalexey@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0515-9785</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Неверов</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Neverov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Неверов Всеволод Анатольевич - канд. техн. наук, научный сотрудник</p><p>107023, г. Москва, ул. Б. Семёновская, д. 38</p><p>Scopus ID: 57196422317</p></bio><bio xml:lang="en"><p>Neverov Vsevolod Anatolyevich - Candidate of Technical Sciences, Research Associate</p><p>38, B. Semyonovskaya St., Moscow, 107023</p><p>Scopus ID: 57196422317</p></bio><email xlink:type="simple">sevasxp@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Научно-технический центр «Автоматизированные технические системы» Московский политехнический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Scientific and Technical Center “Automated Technical Systems” Moscow Polytechnic University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>04</day><month>09</month><year>2026</year></pub-date><volume>23</volume><issue>4</issue><fpage>554</fpage><lpage>566</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Жилейкин М.М., Козелков О.А., Косенков А.А., Неверов В.А., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Жилейкин М.М., Козелков О.А., Косенков А.А., Неверов В.А.</copyright-holder><copyright-holder xml:lang="en">Zhileykin M.M., Kozelkov O.A., Kosenkov A.A., Neverov V.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.sibadi.org/jour/article/view/2311">https://vestnik.sibadi.org/jour/article/view/2311</self-uri><abstract><sec><title>Введение</title><p>Введение. Высокоточное моделирование движения внедорожных и амфибийных транспортных средств основано на точных моделях взаимодействия колес с поверхностью. Несмотря на то, что эмпирические и полуэмпирические модели качения колеса (Пасейки, Го и Лу) доминируют на твердых поверхностях, их входные параметры часто непрозрачны и не имеют прямой физической интерпретации, что существенно ограничивает их прогнозные возможности в сложных многорежимных условиях движения. Часто требуются дорогостоящие и продолжительные испытания конкретных образцов для получения корректных характеристик.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. В данном исследовании представлена экспериментальная проверка физически обоснованной модели динамики колеса для недеформируемых опорных поверхностей. Математическое описание модели шины с использованием щёточной аналогии было приведено в более ранних работах. В качестве среды валидации был использован лабораторный испытательный стенд для измерения кинематики и динамики колеса в широком диапазоне вертикальных нагрузок как в ведомом режиме, так и в ведущем. Ключевые параметры, включая радиус качения, продольное проскальзывание и крутящий момент, измерялись непосредственно на стенде.</p></sec><sec><title>Результаты</title><p>Результаты. Экспериментальные данные были применены для проверки адекватности разработанной математической модели, реализованной в MATLAB/Simulink. Модель продемонстрировала соответствие экспериментам в режиме свободного качения, с нормированной среднеквадратичной ошибкой ниже 1,2% для пройденного расстояния. В режиме движения погрешность увеличилась примерно до 10%, что, согласно анализу, объясняется возросшей сложностью приложения крутящего момента и динамикой проскальзывания.</p></sec><sec><title>Обсуждение и заключение</title><p>Обсуждение и заключение. В отличие от чисто эмпирических моделей все параметры разработанной модели имеют ясный физический смысл и могут быть определены из ограниченного набора экспериментов. Это делает ее предпочтительным выбором для задач, где требуется прогнозирование поведения в различных условиях.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. High-fidelity simulation of off-road and amphibious vehicle motion relies on accurate wheel-surface interaction models. Although empirical and semi-empirical wheel rolling models (Pacejka, Guo and Lu) are dominant on solid surfaces, their input parameters are often ambiguous and do not have a direct physical interpretation, it is significantly limiting their predictive capabilities under complex, multi-mode driving conditions. Expensive and time-consuming specific sample testing is often required to obtain accurate characteristics.</p></sec><sec><title>Materials and Methods</title><p>Materials and Methods. This study presents an experimental validation of a physically based wheel dynamics model for non-deformable supporting surfaces. The mathematical description of the tire model with the use of brush analogy has been previously presented. A laboratory test bench was used as a validation environment to measure wheel kinematics and dynamics under a wide range of vertical loads in both driving and driven modes. Key parameters, including rolling radius, longitudinal slip, and torque have been measured directly on the rig. </p></sec><sec><title>Results</title><p>Results. Experimental data were used to validate the developed mathematical model, implemented in MATLAB/ Simulink. The model demonstrated match with experiment results in free-rolling mode, with a normalized root-meansquare error (RMS) below 1.2% for the covered distance. In driving mode, the error increased to approximately 10%, which, according to the analysis, is explained by the risen complexity of torque application and slip dynamics. </p><p>Discussion and Conclusion. Unlike purely empirical models, all parameters of the developed model have a clear physical meaning and can be determined from a limited set of experiments. It makes this model a preferred choice for problems requiring the behavior prediction under various conditions.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>математическая модель</kwd><kwd>колесный движитель</kwd><kwd>экспериментальная установка</kwd><kwd>моделирование движения</kwd><kwd>колесная машина</kwd><kwd>численное моделирование</kwd><kwd>верификация модели</kwd><kwd>системы стабилизации</kwd><kwd>управление крутящим моментом</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical model</kwd><kwd>wheel propulsion</kwd><kwd>laboratory test bench</kwd><kwd>motion simulation</kwd><kwd>wheeled vehicle</kwd><kwd>numerical simulation</kwd><kwd>model verification</kwd><kwd>stabilization systems</kwd><kwd>torque control</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">материалы статьи подготовлены в рамках научной темы FZRR-2025-0008.</funding-statement><funding-statement xml:lang="en">The materials for this article have been prepared within the framework of scientific research FZRR-2025-0008.</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">Yang S., Lu Y., Li S. An overview on vehicle dynamics //International Journal of Dynamics and Control. 2013. Т. 1. №. 4:385-395. https://doi.org/10.1007/s40435-013-0032-y EDN: ABOTXP</mixed-citation><mixed-citation xml:lang="en">Yang S., Lu Y., Li S. An overview on vehicle dynamics //International Journal of Dynamics and Control. 2013. Т. 1. №. 4:385-395. https://doi.org/10.1007/s40435-013-0032-y EDN: ABOTXP</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, T., Sun, Y., Wang, Y., Li, B., Tian, Y., &amp; Wang, F. Y. A survey of vehicle dynamics modeling methods for autonomous racing: Theoretical models, physical/virtual platforms, and perspectives //IEEE Transactions on Intelligent Vehicles. 2024. Т. 9.№. 3: 4312-4334. https://doi.org/10.1109/tiv.2024.3351131 EDN: LBMDKQ</mixed-citation><mixed-citation xml:lang="en">Zhang, T., Sun, Y., Wang, Y., Li, B., Tian, Y., &amp; Wang, F. Y. A survey of vehicle dynamics modeling methods for autonomous racing: Theoretical models, physical/virtual platforms, and perspectives. IEEE Transactions on Intelligent Vehicles, 2024; 9(3), 4312-4334. https://doi.org/10.1109/tiv.2024.3351131 EDN: LBMDKQ</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Rahnejat, H., Johns-Rahnejat, P. M., Dolatabadi, N., &amp; Rahmani, R. Multi-body dynamics in vehicle engineering //Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics. 2024. Т. 238. №. 1:3-25. https://doi.org/10.1177/1464419323118166</mixed-citation><mixed-citation xml:lang="en">Rahnejat, H., Johns-Rahnejat, P. M., Dolatabadi, N., &amp; Rahmani, R. Multi-body dynamics in vehicle engineering. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics, 2024; 238(1), 3-25. https://doi.org/10.1177/1464419323118166</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Pacejka H. B. (ed.). Tyre models for vehicle dynamics analysis. CRC Press, 2026.</mixed-citation><mixed-citation xml:lang="en">Pacejka, H. B. (Ed.). (2026). Tyre models for vehicle dynamics analysis. CRC Press.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, J., Liu, C., Zhao, J., &amp; Liu, H. Research on stability control of distributed drive vehicle with four-wheel steering //World Electric Vehicle Journal. 2024. Т. 15. №. 6. С. 228. https://doi.org/10.3390/wevj15060228 EDN: IUXMQK</mixed-citation><mixed-citation xml:lang="en">Zhang, J., Liu, C., Zhao, J., Liu, H. Research on stability control of distributed drive vehicle with fourwheel steering. World Electric Vehicle Journal, 2024; 15(6), 228. https://doi.org/10.3390/wevj15060228 EDN: IUXMQK</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Guo K. H., Lu D. The theoretical and experiment study on tire cornering properties under dynamic vertical load //Automot Eng.2005.Т. 27.№. 1.С. 89-92.</mixed-citation><mixed-citation xml:lang="en">Guo K.H., Lu D. The theoretical and experiment study on tire cornering properties under dynamic vertical load. Automot Eng,2005; 27(1), 89-92.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Guo KH Vehicle handling dynamics theory. Jiangsu Science and Technology Press,2011 Nanjing.</mixed-citation><mixed-citation xml:lang="en">Guo, K. H. Vehicle handling dynamics theory. Jiangsu Science and Technology Press, 2011;Nanjing.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Xiong GL, Guo B, Chen XB. Co-simulation and virtual prototyping technology. Tsinghua University Press, 2004; Beijing.</mixed-citation><mixed-citation xml:lang="en">Xiong G.L., Guo, B., Chen, X. B. Co-simulation and virtual prototyping technology.2004; Beijing.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Blundell M., Harty D. The multibody systems approach to vehicle dynamics. Elsevier, 2004.</mixed-citation><mixed-citation xml:lang="en">Blundell M., Harty D. The multibody systems approach to vehicle dynamics.2014; Butterworth-Heinemann.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Luigi Romano, Ole Morten Aamo, Jan Aslund &amp; Erik Frisk Stability analysis of linear single-track models with transient tyre dynamics, Vehicle System Dynamics, 2026; 64:3, 611-645, https://doi.org/10.1080/00423114.2024.2445163</mixed-citation><mixed-citation xml:lang="en">Romano L., Aamo O.M., Aslund J., Frisk E. Stability analysis of linear single-track models with transient tyre dynamics. Vehicle System Dynamics, 2026; 64(3), 611-645. https://doi.org/10.1080/00423114.2024.2445163</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">H Guo, Z Yin, D Cao, H Chen, C Lv. “A Re-view of Estimation for Vehicle Tire-Road Interactions Toward Automated Driving”, in IEEE Transactions on Systems, Man, and Cybernetics: Systems. Jan. 2019; 49(1): 14-30.</mixed-citation><mixed-citation xml:lang="en">Guo H., Yin Z., Cao D., Chen H., Lv C. A review of estimation for vehicle tire-road interactions toward automated driving. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018; 49(1), 14-30. https://doi.org/10.1109/TSMC.2018.2819500</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Kobayashi T. Development of inverse magic formula for tire performance requirement analysis // Transactions of Society of Automotive Engineers of Japan. 2022. Т. 53. №. 5. С. 936-941.</mixed-citation><mixed-citation xml:lang="en">Kobayashi T. Development of inverse magic formula for tire performance requirement analysis. Transactions of Society of Automotive Engineers of Japan, 2022; 53(5), 936-941.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Решмин С.А. Качественный анализ силы тяги при вращении ведущего колеса с невесомой шиной. Оптимальное управление и дифференциальные игры, Сборник статей, Труды МИАН, 315, МИАН, М., 2021, 211–221; Proc. Steklov Inst. Math., 315 (2021), 198–208. https://doi.org/10.4213/tm4222.</mixed-citation><mixed-citation xml:lang="en">Reshmin S.A. Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire. Proc. Steklov Inst. Math. 315, 198–208 (2021). (in Russ.) https://doi.org/10.1134/S0081543821050151</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Киреенков А.А., Жаворонок С.И., Нуштаев Д.В. О моделях шины, учитывающих как деформированное состояние, так и эффекты сухого трения в области контакта // Компьютерные исследования и моделирование, 2021. Т. 13, № 1. С. 163–173. https://doi.org/10.20537/2076-7633-2021-13-1-163-173. URL: http://crm.ics.org.ru/journal/article/3034/ (дата обращения: 24.06.2026).</mixed-citation><mixed-citation xml:lang="en">Kireenkov A.A., Zhavoronok S.I., Nushtaev D.V. On tire models accounting for both deformed state and coupled dry friction in a contact spot // Computer Research and Modeling, 2021, vol. 13, no. 1, pp. 163-173. (in Russ.) https://doi.org/10.20537/2076-7633-2021-13-1-163-173. URL: http://crm.ics.org.ru/journal/article/3034/ (date accessed: 24.06.2026)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Fathi H., El-Sayegh Z., Ren J., El-Gindy M. Modeling and validation of a passenger car tire using finite element analysis //Vehicles. 2024. Т. 6. №. 1. С. 384-402. https://doi.org/10.3390/vehicles6010016 EDN: RTTLIG</mixed-citation><mixed-citation xml:lang="en">Fathi H., El-Sayegh Z., Ren J., El-Gindy M. Modeling and validation of a passenger car tire using finite element analysis. Vehicles,2024. 6(1), 384-402. https://doi.org/10.3390/vehicles6010016 EDN: RTTLIG</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Behroozi M., Olatunbosun O.A., Ding W. Finite element analysis of aircraft tyre-Effect of model complexity on tyre performance characteristics //Materials &amp; Design. 2012. Т. 35. С. 810-819.</mixed-citation><mixed-citation xml:lang="en">Behroozi M., Olatunbosun, O.A., Ding, W. Finite element analysis of aircraft tyre–Effect of model complexity on tyre performance characteristics. Materials &amp; Design, 2012; 35, 810-819.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Fathi H. et al. An advancement in trucktire-road interaction using the finite element analysis //Mathematics. - 2023. Т. 11. - №. 11. С. 2462. DOI: 10.3390/math11112462 EDN: YFFSEU</mixed-citation><mixed-citation xml:lang="en">Fathi H., Khosravi M., El-Sayegh Z., El-Gindy, M. An advancement in truck-tire–road interaction using the finite element analysis. Mathematics, 2023; 11(11), 2462. https://doi.org/10.3390/math11112462 EDN: YFFSEU</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Jagadeesh A., Premarathna W.A. A.S., Kumar A., Kasbergen, C., Erkens S.M.J. G. Finite element modelling of jointed plain concrete pavements under rolling forklift tire //Engineering Structures. 2025. Т. 328. С. 119705. https://doi.org/10.1016/j.eng-struct.2025.119705 EDN: XWLRMI</mixed-citation><mixed-citation xml:lang="en">Jagadeesh A., Premarathna W.A.A.S., Kumar A., Kasbergen C., Erkens S.M.J.G. Finite element modelling of jointed plain concrete pavements under rolling forklift tire. Engineering Structures, 2025; 328, 119705. https://doi.org/10.1016/j.eng-struct.2025.119705 EDN: XWLRMI</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Ge Y., Yan Y., Yan X., Meng Z. Extending the tire dynamic model range of operating conditions based on finite element method //Advances in Mechanical Engineering. 2022. Т. 14. №. 3. С. 16878132221085454.</mixed-citation><mixed-citation xml:lang="en">Ge Y., Yan Y., Yan X., Meng Z. Extending the tire dynamic model range of operating conditions based on finite element method. Advances in Mechanical Engineering, 2022; 14(3), 16878132221085454.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Yamashita H., Arnold A., Carrica P. M., Noack R. W., Martin J. E., Sugiyama H., Harwood C. Coupled multibody dynamics and computational fluid dynamics approach for amphibious vehicles in the surf zone //Ocean engineering. 2022. Т. 257. С. 111607. https://doi.org/10.1016/j.oceaneng.2022.111607 EDN: OUBLAN</mixed-citation><mixed-citation xml:lang="en">Yamashita H., Arnold A., Carrica P.M., Noack R.W., Martin J.E., Sugiyama H., Harwood C. Coupled multibody dynamics and computational fluid dynamics approach for amphibious vehicles in the surf zone. Ocean engineering, 2022; 257, 111607. https://doi.org/10.1016/j.oceaneng.2022.111607 EDN: OUBLAN</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Жилейкин М.М., Падалкин Б.В. Математическая модель качения эластичного колеса по неровностям недеформируемого основания // Известия ВУЗОВ. Машиностроение.2016. № 3. С. 24–29. EDN: VOJFZZ</mixed-citation><mixed-citation xml:lang="en">Zhileikin M.M., Padalki B.V. “A Mathematical Model of Rolling of an Elastic Wheel on Irregularities of a Non-Deformable Support Foundation.” News of Higher Educational Institutions. Mechanical Engineering 3 (672) (2016): 24–29. (in Russ.) EDN: VOJFZZ</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Жилейкин М.М., Козелков О.А., Неверов В.А. Математическая модель качения по неровностям опорного основания эластичного колеса на базе дискретного набора контактных элементов // Грузовик. 2025. № 6. С. 8–16. https://doi.org/10.36652/1684-1298-2025-6-8-16. EDN BAVNVA.</mixed-citation><mixed-citation xml:lang="en">Zhileikin M.M., Kozelkov O.A., Neverov V.A. Mathematical model of rolling on uneven support base of an elastic wheel based on a discrete set of contact elements. Gruzovik. 2025. No. 6. P. 8-16. (in Russ.) https://doi.org/10.36652/1684-1298-2025-6-8-16.  EDN: BAVNVA.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Neil D. Bennett, Barry F.W. Croke, Giorgio Guariso, Joseph H.A. Guillaume, Serena H. Hamilton, Anthony J. Jakeman, Stefano Marsili-Libelli, Lachlan T.H. Newham, John P. Norton, Charles Perrin, Suzanne A. Pierce, Barbara Robson, Ralf Seppelt, Alexey A. Voinov, Brian D. Fath, Vazken Andreassian. Characterising performance of environmental models //Environmental modelling &amp; software. 2013. Т. 40. С. 1-20. https://doi.org/10.1016/j.envsoft.2012.09.011</mixed-citation><mixed-citation xml:lang="en">Neil D. Bennett, Barry F.W. Croke, Giorgio Guariso, Joseph H.A. Guillaume, Serena H. Hamilton, Anthony J. Jakeman, Stefano Marsili-Libelli, Lachlan T.H. Newham, John P. Norton, Charles Perrin, Suzanne A. Pierce, Barbara Robson, Ralf Seppelt, Alexey A. Voinov, Brian D. Fath, Vazken Andreassian. Characterising performance of environmental models. Environmental modelling &amp; software, 2013; 40, 1-20. https://doi.org/10.1016/j.envsoft.2012.09.011</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Z., Liu Y., Gao Q. In-plane flexible ring modeling and a nonlinear stiffness solution for heavy-load radial tires //Mechanical Systems and Signal Processing. 2022. Т. 171. С. 108956. https://doi.org/10.1016/j.ymssp.2022.108956 EDN: MBMMDO</mixed-citation><mixed-citation xml:lang="en">Liu Z., Liu Y., Gao Q. In-plane flexible ring modeling and a nonlinear stiffness solution for heavyload radial tires. Mechanical Systems and Signal Processing, 2022; 171, 108956. https://doi.org/10.1016/j.ymssp.2022.108956 EDN: MBMMDO</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Xia D., Liu Q., Lu D. Friction prediction and application to lateral or longitudinal slip force prediction //Machines. 2022. Т. 10. №. 9.С. 791. https://doi.org/10.3390/machines10090791 EDN: PENJSI</mixed-citation><mixed-citation xml:lang="en">Xia D., Liu Q., Lu D. Friction prediction and application to lateral or longitudinal slip force prediction. Machines, 2022; 10(9), 791. https://doi.org/10.3390/machines10090791 EDN: PENJSI</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Junior A.D.S., Birkner C., Jazar R. N., Marzbani H. Coupled lateral and longitudinal controller for over-actuated vehicle in evasive maneuvering with sliding mode control strategy // IEEE Access. 2023. Т. 11. С. 33792-33811. https://doi.org/10.1109/access.2023.3264277 EDN: GNPOKM</mixed-citation><mixed-citation xml:lang="en">Junior A.D.S., Birkner C., Jazar R.N., Marzbani H. Coupled lateral and longitudinal controller for over-actuated vehicle in evasive maneuvering with sliding mode control strategy. IEEE Access, 2023; 11, 33792-33811. https://doi.org/10.1109/access.2023.3264277 EDN: GNPOKM</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>
