Antali Mate, Stepan Gabor
Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, 1521 Hungary.
Nonlinear Dyn. 2019;97(3):1799-1817. doi: 10.1007/s11071-019-04913-x. Epub 2019 Apr 4.
In this paper, the nonsmooth dynamics of two contacting rigid bodies is analysed in the presence of dry friction. In three dimensions, slipping can occur in continuously many directions. Then, the Coulomb friction model leads to a system of differential equations, which has a codimension-2 discontinuity set in the phase space. The new theory of extended Filippov systems is applied to analyse the dynamics of a rigid body moving on a fixed rigid plane to explore the possible transitions between the slipping and rolling behaviour. The paper focuses on finding the so-called limit directions of the slipping equations at the discontinuity. This leads to a complete qualitative description of the possible scenarios of the dynamics in the vicinity of the discontinuity. It is shown that the new approach consistently extends the information provided from the static friction force of the rolling behaviour. The methods are demonstrated on an application example.
本文分析了存在干摩擦时两个接触刚体的非光滑动力学。在三维空间中，滑动可沿连续多个方向发生。于是，库仑摩擦模型导致了一个微分方程组，该方程组在相空间中具有余维数为2的间断集。应用扩展 Filippov 系统的新理论来分析刚体在固定刚性平面上运动的动力学，以探索滑动和滚动行为之间可能的转变。本文重点在于找出间断处滑动方程的所谓极限方向。这导致了对间断附近动力学可能情形的完整定性描述。结果表明，新方法持续扩展了由滚动行为的静摩擦力提供的信息。通过一个应用实例展示了这些方法。
