On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone
Background. Current research on the properties of brachistochrones as lines with extreme properties indicates that this work is relevant because it takes into account for the first time the influence of thermal effects on the shape of the brachistochrone. The purpose of the study is an analytically...
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2025-06-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| _version_ | 1849329199436791808 |
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| author | S.O. Gladkov S.B. Bogdanova |
| author_facet | S.O. Gladkov S.B. Bogdanova |
| author_sort | S.O. Gladkov |
| collection | DOAJ |
| description | Background. Current research on the properties of brachistochrones as lines with extreme properties indicates that this work is relevant because it takes into account for the first time the influence of thermal effects on the shape of the brachistochrone. The purpose of the study is an analytically rigorous solution to the problem. Matherials and methods. The main method for solving the problem is the moving basis method, which has proven itself well in solving many problems related to the study of various properties of brachistochrones. Results. A rigorous analytical solution of the formulated problem is given, taking into account the thermal effect, which was taken into account by introducing a dissipative function. Conclusions. Thanks to the algorithm proposed in the article, a general methodological approach has been formulated that is useful in solving such problems related to taking into account the thermal properties of materials. |
| format | Article |
| id | doaj-art-fedbe16a28ea4d56b37128b63f92042b |
| institution | Kabale University |
| issn | 2072-3040 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| spelling | doaj-art-fedbe16a28ea4d56b37128b63f92042b2025-08-20T03:47:20ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки2072-30402025-06-01110.21685/2072-3040-2025-1-3On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone S.O. Gladkov0S.B. Bogdanova1Moscow Aviation Institute (National Research University)Moscow Aviation Institute (National Research University)Background. Current research on the properties of brachistochrones as lines with extreme properties indicates that this work is relevant because it takes into account for the first time the influence of thermal effects on the shape of the brachistochrone. The purpose of the study is an analytically rigorous solution to the problem. Matherials and methods. The main method for solving the problem is the moving basis method, which has proven itself well in solving many problems related to the study of various properties of brachistochrones. Results. A rigorous analytical solution of the formulated problem is given, taking into account the thermal effect, which was taken into account by introducing a dissipative function. Conclusions. Thanks to the algorithm proposed in the article, a general methodological approach has been formulated that is useful in solving such problems related to taking into account the thermal properties of materials. : brachystochronegradient of temperatureheat capacitymovable basisequations of motion |
| spellingShingle | S.O. Gladkov S.B. Bogdanova On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone Известия высших учебных заведений. Поволжский регион: Физико-математические науки : brachystochrone gradient of temperature heat capacity movable basis equations of motion |
| title | On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone |
| title_full | On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone |
| title_fullStr | On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone |
| title_full_unstemmed | On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone |
| title_short | On a strict mathematical definition of the brachistochrone’s shape taking into account the thermal effect in the contact zone |
| title_sort | on a strict mathematical definition of the brachistochrone s shape taking into account the thermal effect in the contact zone |
| topic | : brachystochrone gradient of temperature heat capacity movable basis equations of motion |
| work_keys_str_mv | AT sogladkov onastrictmathematicaldefinitionofthebrachistochronesshapetakingintoaccountthethermaleffectinthecontactzone AT sbbogdanova onastrictmathematicaldefinitionofthebrachistochronesshapetakingintoaccountthethermaleffectinthecontactzone |