Asymptotic analysis of Painleve&apos;s paradox

doi:10.1007/s11044-014-9448-1

CORC > 北京大学 > 工学院

	Asymptotic analysis of Painleve's paradox
	Zhao, Zhen ; Liu, Caishan ; Chen, Bin ; Brogliato, Bernard
刊名	MULTIBODY SYSTEM DYNAMICS
	2015
关键词	Painleve paradox Coulomb&apos Singularity RIGID-BODY DYNAMICS DRY FRICTION CONTACT IMPACT SYSTEMS CONSTRAINTS STABILITY MOTION MODELS s friction
DOI	10.1007/s11044-014-9448-1
英文摘要	Painleve's paradox is a well-known problem in rigid-body dynamics, of which the forward dynamics equations could have no solution. To handle this situation, an assumption of tangential impact is often introduced. Although the assumption seems to provide a good fix, it still needs to be mathematically examined via analyzing the asymptotic property of a compliance-based model at the limit of rigidity. In this paper, we revisit the paradox using the typical Painleve's example of a rod sliding on a rough surface. For convenience, the interaction at the contact point of the rod is represented by a linear spring to scale the local normal compliance, coupled with Coulomb's law to reflect friction. We perform an asymptotic analysis using the spring stiffness as a perturbation parameter. The rod dynamics in the Painlev,'s paradox, accompanying the variation of friction status, consists of three distinct phases as follows: An initial period of sliding which allows contact force to diverge with the increase of the spring stiffness, a period of sticking which ends at the occurrence of a reverse slip motion, and a reverse slip phase which causes the rod to be detached from the contact surface. As the stiffness goes to infinity, all the time intervals of the three phases converge to zero. This analysis theoretically confirms the assumption of the tangential impact in the paradox of sliding rod dynamics.; Natural Science Foundation of China [11172019, 11132001, 11472011]; 'Fanzhou' Youth Research Foundation [20110501]; SCI(E); EI; ARTICLE; bhzhaozhen@buaa.edu.cn; liucs@pku.edu.cn; bernard.brogliato@inria.fr; 3; 299-319; 35
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/415463]
专题	工学院
推荐引用方式 GB/T 7714	Zhao, Zhen,Liu, Caishan,Chen, Bin,et al. Asymptotic analysis of Painleve's paradox[J]. MULTIBODY SYSTEM DYNAMICS,2015.
APA	Zhao, Zhen,Liu, Caishan,Chen, Bin,&Brogliato, Bernard.(2015).Asymptotic analysis of Painleve's paradox.MULTIBODY SYSTEM DYNAMICS.
MLA	Zhao, Zhen,et al."Asymptotic analysis of Painleve's paradox".MULTIBODY SYSTEM DYNAMICS (2015).