[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j140298

CONTROLLABILITY OF ROLLING BODIES WITH REGULAR SURFACES

Moghadasi, S. Reza (Department of Mathematical Science Sharif University of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 725-735 More about this Journal

Abstract

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. There is a geometric condition equivalent to the rolling constraint which enables us to generalize the rolling motions for any two-dimensional Riemannian manifolds. This system has a five-dimensional phase space. In order to study the controllability of the rolling surfaces, we lift the system to a six-dimensional space and show that the lifted system is controllable unless the two surfaces have isometric universal covering spaces. In the non-controllable case there are some three-dimensional orbits each of which corresponds to an isometry of the universal covering spaces.

Keywords

controllability; rolling bodies; geodesic curvature; isometry group;

Citations & Related Records

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