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Technical Brief

Semistability Analysis of the Chaplygin Sleigh and Nonsmooth Mechanical Oscillator

[+] Author and Article Information
N. Sai Pushpak

Dynamics and Control Laboratory,
Department of Electrical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: saipushpak.n@gmail.com

Arun D. Mahindrakar

Dynamics and Control Laboratory,
Department of Electrical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: arun_dm@iitm.ac.in

Anup Ekbote

Dynamics and Control Laboratory,
Department of Electrical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: anupekbote@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 14, 2013; final manuscript received January 29, 2014; published online March 11, 2014. Assoc. Editor: Prashant Mehta.

J. Dyn. Sys., Meas., Control 136(3), 034505 (Mar 11, 2014) (4 pages) Paper No: DS-13-1198; doi: 10.1115/1.4026653 History: Received May 14, 2013; Revised January 29, 2014

An appropriate notion for stability studies of dynamical systems with a continuum of equilibria is semistability. One approach to semistability investigation is based on the nontangency between the vector field and the set of equilibria. In this work, we introduce a novel way of verifying nontangency by computing an outer estimate of the direction cone and illustrate its application through two well-known second-order systems. The stable equilibria of both the systems are shown to possess the semistability property.

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References

Figures

Grahic Jump Location
Fig. 1

Overbounding sets under the map f

Grahic Jump Location
Fig. 2

Tangent cone, direction cone, and F∧x

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