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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Main Authors: S.O. Gladkov, S.B. Bogdanova
Format: Article
Language:English
Published: Penza State University Publishing House 2025-06-01
Series:Известия высших учебных заведений. Поволжский регион: Физико-математические науки
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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.
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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
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