NDLI: Contact constraints and dynamical equations in Lagrangian systems

Content Provider	Springer Nature Link
Author	Zhao, Zhen Liu, Caishan
Copyright Year	2016
Abstract	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.
Starting Page	77
Ending Page	99
Page Count	23
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	38
Issue Number	1
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-01-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Contact Constraints Dynamics Lagrangian system Vibration, Dynamical Systems, Control Optimization Electrical Engineering Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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