{"title":"The Tippedisk: A Minimal Model For Friction-Induced Inversion","authors":"Simon Sailer, S. Eugster, R. Leine","doi":"10.3311/eccomasmbd2021-113","DOIUrl":null,"url":null,"abstract":"The tippedisk is a new mechanical-mathematical archetype for friction induced insta-bility phenomena, showing an inversion similar to the inversion of the tippetop. Un-like the tippetop, the tippedisk has no rotational symmetry, which greatly complicates its analysis. Since the system cannot be reduced to a planar one, one has to consider the full three-dimensional kinematics, being intrinsically nonlinear. In this work a new minimal model is derived that contains the main relevant physical effects so that the inversion phenomenon can be described qualitatively. The in-depth analysis leads to slow-fast systems with homoclinic connections and global bifurcations.","PeriodicalId":431921,"journal":{"name":"Proceedings of the 10th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 10th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3311/eccomasmbd2021-113","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The tippedisk is a new mechanical-mathematical archetype for friction induced insta-bility phenomena, showing an inversion similar to the inversion of the tippetop. Un-like the tippetop, the tippedisk has no rotational symmetry, which greatly complicates its analysis. Since the system cannot be reduced to a planar one, one has to consider the full three-dimensional kinematics, being intrinsically nonlinear. In this work a new minimal model is derived that contains the main relevant physical effects so that the inversion phenomenon can be described qualitatively. The in-depth analysis leads to slow-fast systems with homoclinic connections and global bifurcations.
tip - disk是研究摩擦不稳定现象的一种新的力学数学原型，它表现出类似于tip - top的反转。与陀螺不同的是，陀螺盘没有旋转对称性，这使分析变得非常复杂。由于系统不能简化为平面系统，必须考虑完整的三维运动学，本质上是非线性的。在这项工作中，导出了一个新的最小模型，其中包含了主要的相关物理效应，从而可以定性地描述反转现象。深入分析得到了具有同斜连接和全局分岔的慢速系统。
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