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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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
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| Zusammenfassung: | 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.  |
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| DOI: | 10.3842/umzh.v76i8.7596 |