A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$
UDC 531 We propose a generalization for the sliding-rolling motion, which leads to meaningful physical and mathematical results as the general metric includes the time dimension. We also investigate the kinematics of the relative motion of two rigid objects, which maintain sliding-rolli...
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| Datum: | 2024 |
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| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7596 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512688577183744 |
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| author | Şahin, Tevfik Orbay, Keziban Özdemir, Zehra Şahin, Tevfik Orbay, Keziban Özdemir, Zehra |
| author_facet | Şahin, Tevfik Orbay, Keziban Özdemir, Zehra Şahin, Tevfik Orbay, Keziban Özdemir, Zehra |
| author_sort | Şahin, Tevfik |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-09-25T06:57:29Z |
| description | UDC 531
We propose a generalization for the sliding-rolling motion, which leads to meaningful physical and mathematical results as the general metric includes the time dimension. We also investigate the kinematics of the relative motion of two rigid objects, which maintain sliding-rolling contact, by using the general adjoint approach in the semi-Euclidean space  $\mathbb{R}_{\varepsilon}^{3},$ where $\varepsilon \in \{0,1\}.$ This generalization gives  the geometric kinematic equations of the sliding-rolling motion in Minkowski and Euclidean spaces. In these spaces, we get a set of overconstrained equations. Solving this system, we determine translational and angular velocities of the moving surface.
 Finally, we illustrate the results by two examples.  |
| doi_str_mv | 10.3842/umzh.v76i8.7596 |
| first_indexed | 2026-03-24T03:32:46Z |
| format | Article |
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| id | umjimathkievua-article-7596 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:46Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-75962024-09-25T06:57:29Z A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ Şahin, Tevfik Orbay, Keziban Özdemir, Zehra Şahin, Tevfik Orbay, Keziban Özdemir, Zehra Rolling-sliding motion Contact Adjoint Kinematics Differential geometry semi-Euclidean space Geometry & Topology, Fractals UDC 531 We propose a generalization for the sliding-rolling motion, which leads to meaningful physical and mathematical results as the general metric includes the time dimension. We also investigate the kinematics of the relative motion of two rigid objects, which maintain sliding-rolling contact, by using the general adjoint approach in the semi-Euclidean space  $\mathbb{R}_{\varepsilon}^{3},$ where $\varepsilon \in \{0,1\}.$ This generalization gives  the geometric kinematic equations of the sliding-rolling motion in Minkowski and Euclidean spaces. In these spaces, we get a set of overconstrained equations. Solving this system, we determine translational and angular velocities of the moving surface.  Finally, we illustrate the results by two examples.  УДК 531 Узагальнення кінематики руху ковзання-кочення в напівевклідовому просторі $\mathbb{R}_\varepsilon^3$ Наведено узагальнення для руху ковзання-кочення, яке дає вагомі фізичні і математичні результати, оскільки загальна метрика включає часовий вимір. Також досліджено кінематику відносного руху двох твердих об’єктів, що підтримують контакт ковзання-кочення, за допомогою загального спряженого підходу у напівевклідовому просторі $\mathbb{R}_{\varepsilon}^{3},$ де $\varepsilon \in \{0,1\}.$  Запропоноване узагальнення дає  геометричні кінематичні рівняння руху ковзання-кочення у просторах Мінковського та Евкліда. У цих просторах отримано систему рівнянь із надмірними обмеженнями. Розв’язуючи цю систему, ми визначаємо поступальну та кутову швидкості рухомої поверхні.  Насамкінець отримані результати проілюстровано двома прикладами. Institute of Mathematics, NAS of Ukraine 2024-09-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7596 10.3842/umzh.v76i8.7596 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 8 (2024); 1235 - 1249 Український математичний журнал; Том 76 № 8 (2024); 1235 - 1249 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7596/10158 Copyright (c) 2024 Tevfik Şahin |
| spellingShingle | Şahin, Tevfik Orbay, Keziban Özdemir, Zehra Şahin, Tevfik Orbay, Keziban Özdemir, Zehra A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_alt | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_full | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_fullStr | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_full_unstemmed | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_short | A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$ |
| title_sort | generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{r}_\varepsilon^3$ |
| topic_facet | Rolling-sliding motion Contact Adjoint Kinematics Differential geometry semi-Euclidean space Geometry & Topology Fractals |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7596 |
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