Generalization for the Kinematics of Sliding-Rolling Motion in the Semi-Euclidean Space \({\mathbb{R}}_{\varepsilon }^{3}\)

We propose a generalization for the sliding-rolling motion, which leads to meaningful physical and mathematical results because the general metric includes the time dimension. We also study the kinematics of the relative motion of two rigid objects maintaining sliding-rolling contact, by using the general adjoint approach in the semi-Euclidean space \({\mathbb{R}}_{\varepsilon }^{3},\) ${\mathbb{R}}_{\epsilon }^3,$ where ε ∈ {0, 1}. This generalization gives the geometric kinematic equations of the sliding-rolling motion in the Minkowski and Euclidean spaces. In these spaces, we get a set of overconstrained equations. Solving this system, we determine the translational and angular velocities of the moving surface. Finally, we illustrate the results by two examples.