Precise solution of the brachistochrone curve problem taking into account the dry friction force
Background. Currently, there is quite a lot of competition among scientific groups dealing with issues related to brachistochrone, so our study, based on the idea of a mobile basis, is quite relevant to the present time, especially since the purpose of the study is to find an accurate solution to dy...
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2023-09-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| _version_ | 1797737592964251648 |
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| author | Sergey O. Gladkov |
| author_facet | Sergey O. Gladkov |
| author_sort | Sergey O. Gladkov |
| collection | DOAJ |
| description | Background. Currently, there is quite a lot of competition among scientific groups dealing with issues related to brachistochrone, so our study, based on the idea of a mobile basis, is quite relevant to the present time, especially since the purpose of the study is to find an accurate solution to dynamic equations taking into account dry friction on the trough. Materials and methods. The research method is based on the theory of the mobile basis, repeatedly tested on a set of problems relating to curvilinear motion. Results. Using the movable basis method, the equations of motion of the ball along the chute are obtained without taking into account slippage, but taking into account the force of dry friction. The exact solution of the problem in parametric form for the case was found μ ≠ 0 . Conclusions. The proposed approach made it possible to find an accurate analytical solution to the brachistochrone problem, taking into account the forces of dry friction. |
| first_indexed | 2024-03-12T13:31:38Z |
| format | Article |
| id | doaj.art-99f45139875f420192b921d620870dd3 |
| institution | Directory Open Access Journal |
| issn | 2072-3040 |
| language | English |
| last_indexed | 2024-03-12T13:31:38Z |
| publishDate | 2023-09-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| spelling | doaj.art-99f45139875f420192b921d620870dd32023-08-24T11:00:49ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки2072-30402023-09-01210.21685/2072-3040-2023-2-1Precise solution of the brachistochrone curve problem taking into account the dry friction forceSergey O. Gladkov0Moscow aviation instituteBackground. Currently, there is quite a lot of competition among scientific groups dealing with issues related to brachistochrone, so our study, based on the idea of a mobile basis, is quite relevant to the present time, especially since the purpose of the study is to find an accurate solution to dynamic equations taking into account dry friction on the trough. Materials and methods. The research method is based on the theory of the mobile basis, repeatedly tested on a set of problems relating to curvilinear motion. Results. Using the movable basis method, the equations of motion of the ball along the chute are obtained without taking into account slippage, but taking into account the force of dry friction. The exact solution of the problem in parametric form for the case was found μ ≠ 0 . Conclusions. The proposed approach made it possible to find an accurate analytical solution to the brachistochrone problem, taking into account the forces of dry friction.brachystochronedry friction forcemobile basisreaction force |
| spellingShingle | Sergey O. Gladkov Precise solution of the brachistochrone curve problem taking into account the dry friction force Известия высших учебных заведений. Поволжский регион: Физико-математические науки brachystochrone dry friction force mobile basis reaction force |
| title | Precise solution of the brachistochrone curve problem taking into account the dry friction force |
| title_full | Precise solution of the brachistochrone curve problem taking into account the dry friction force |
| title_fullStr | Precise solution of the brachistochrone curve problem taking into account the dry friction force |
| title_full_unstemmed | Precise solution of the brachistochrone curve problem taking into account the dry friction force |
| title_short | Precise solution of the brachistochrone curve problem taking into account the dry friction force |
| title_sort | precise solution of the brachistochrone curve problem taking into account the dry friction force |
| topic | brachystochrone dry friction force mobile basis reaction force |
| work_keys_str_mv | AT sergeyogladkov precisesolutionofthebrachistochronecurveproblemtakingintoaccountthedryfrictionforce |