Contact constraints and dynamical equations in Lagrangian systems

doi:10.1007/s11044-016-9503-1

CORC > 北京大学 > 工学院

	Contact constraints and dynamical equations in Lagrangian systems
	Zhao, Zhen ; Liu, Caishan
刊名	MULTIBODY SYSTEM DYNAMICS
	2016
关键词	Contact Constraints Dynamics Lagrangian system RIGID BODIES MOTION
DOI	10.1007/s11044-016-9503-1
英文摘要	Constraints work in the simplest way among a variety of methods of modeling the mechanical behaviors on the interface between bodies. The constraints within a persistent point contact usually fall into the following three categories: geometry-dependent constraints due to non-penetration limitation between the two rigid bodies; velocity- or force-dependent constraints due to the vanishing of tangential velocity or sliding friction engaged in tangential interaction. Though those constraints may be intuitively obtained for some simple problems, they are essentially associated with the evolution of location parameters denoting the temporal position of the contact point. Focusing on a multibody system subject to a persistent point contact, we propose a uniform and programmable procedure to formulate the constraint equations. Kinematic analysis along the procedure can clearly expose the dependence of the constraint equations on the location parameters, unveil the reason why the velocity-dependent constraints may become nonholonomic, and exhibit the fulfillment of the Appell-Chetaev's rule naturally. Furthermore, we employ d'Alembert-Lagrangian principle to yield the dynamical equations of the system via the method of Lagrange's multipliers. The dynamical equations so obtained are then compared with those derived from a quite different method that characterizes the contact interplay as a pair of contact force vectors. Accordingly, the correlations between the Lagrange multipliers and the components of the real contact force can be clarified. The clarification enables us to correctly embed the force-dependent constraints into the dynamical equations. A classical example of a thin disk contacting a horizontal rough surface is provided to demonstrate the validation of the proposed theory and method.; NSFC [11172019, 11132001, 11472011]; SCI(E); EI; ARTICLE; bhzhaozhen@buaa.edu.cn; liucs@pku.edu.cn; 1; 77-99; 38
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/491507]
专题	工学院
推荐引用方式 GB/T 7714	Zhao, Zhen,Liu, Caishan. Contact constraints and dynamical equations in Lagrangian systems[J]. MULTIBODY SYSTEM DYNAMICS,2016.
APA	Zhao, Zhen,&Liu, Caishan.(2016).Contact constraints and dynamical equations in Lagrangian systems.MULTIBODY SYSTEM DYNAMICS.
MLA	Zhao, Zhen,et al."Contact constraints and dynamical equations in Lagrangian systems".MULTIBODY SYSTEM DYNAMICS (2016).