Two-factor optimization in the brachistochrone problem
The paper puts forward a new modification of the well-known brachistochrone problem. The joint account of minimizing the motion time and the trajectory length in their functional relationship has been introduced. A two-factor optimization criterion (TOC) was constructed in the form of a product of t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2022-06-01
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| Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| Subjects: | |
| Online Access: | https://physmath.spbstu.ru/article/2022.56.11/ |
| _version_ | 1811325111133798400 |
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| author | Smirnov Alexey Suvorov Sergei |
| author_facet | Smirnov Alexey Suvorov Sergei |
| author_sort | Smirnov Alexey |
| collection | DOAJ |
| description | The paper puts forward a new modification of the well-known brachistochrone problem. The joint account of minimizing the motion time and the trajectory length in their functional relationship has been introduced. A two-factor optimization criterion (TOC) was constructed in the form of a product of two particular criteria, which made it possible to find the best compromise between them. On the TOC basis a solution to the problem of a two-factor brachistochrone was obtained using a preliminary consideration of the auxiliary problem on a brachistochrone with a given length. A rational practical solution of the problem was proposed. It was characterized by a simpler geometry than the strictly optimal one: to adopt a circular arc with a central angle selected on the basis of the taken TOC. |
| first_indexed | 2024-04-13T14:27:19Z |
| format | Article |
| id | doaj.art-73ef3d74f80d45268d7a5b6ed2cf4f1b |
| institution | Directory Open Access Journal |
| issn | 2405-7223 |
| language | English |
| last_indexed | 2024-04-13T14:27:19Z |
| publishDate | 2022-06-01 |
| publisher | Peter the Great St.Petersburg Polytechnic University |
| record_format | Article |
| series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| spelling | doaj.art-73ef3d74f80d45268d7a5b6ed2cf4f1b2022-12-22T02:43:17ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232022-06-0115210.18721/JPM.1521120714726Two-factor optimization in the brachistochrone problemSmirnov Alexey0https://orcid.org/0000-0002-6148-0322Suvorov Sergei1https://orcid.org/0000-0002-7461-2742Peter the Great St. Petersburg Polytechnic UniversityCentral Design Bureau of Transport EngineeringThe paper puts forward a new modification of the well-known brachistochrone problem. The joint account of minimizing the motion time and the trajectory length in their functional relationship has been introduced. A two-factor optimization criterion (TOC) was constructed in the form of a product of two particular criteria, which made it possible to find the best compromise between them. On the TOC basis a solution to the problem of a two-factor brachistochrone was obtained using a preliminary consideration of the auxiliary problem on a brachistochrone with a given length. A rational practical solution of the problem was proposed. It was characterized by a simpler geometry than the strictly optimal one: to adopt a circular arc with a central angle selected on the basis of the taken TOC.https://physmath.spbstu.ru/article/2022.56.11/brachistochroneoptimizationmotion timetrajectory lengthtwo-factor criterionrational solution |
| spellingShingle | Smirnov Alexey Suvorov Sergei Two-factor optimization in the brachistochrone problem St. Petersburg Polytechnical University Journal: Physics and Mathematics brachistochrone optimization motion time trajectory length two-factor criterion rational solution |
| title | Two-factor optimization in the brachistochrone problem |
| title_full | Two-factor optimization in the brachistochrone problem |
| title_fullStr | Two-factor optimization in the brachistochrone problem |
| title_full_unstemmed | Two-factor optimization in the brachistochrone problem |
| title_short | Two-factor optimization in the brachistochrone problem |
| title_sort | two factor optimization in the brachistochrone problem |
| topic | brachistochrone optimization motion time trajectory length two-factor criterion rational solution |
| url | https://physmath.spbstu.ru/article/2022.56.11/ |
| work_keys_str_mv | AT smirnovalexey twofactoroptimizationinthebrachistochroneproblem AT suvorovsergei twofactoroptimizationinthebrachistochroneproblem |