TY - JOUR
AU - Tevfik Şahin
AU - Keziban Orbay
AU - Zehra Özdemir
PY - 2024/09/04
Y2 - 2024/10/11
TI - A generalization for the kinematics of sliding-rolling motion in the semi-euclidean space $\mathbb{R}_\varepsilon^3$
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 76
IS - 8
SE - Research articles
DO - 10.3842/umzh.v76i8.7596
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7596
AB - UDC 531We 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.
ER -