J. Korean Math. Soc. 2016; 53(4): 725-735
Printed July 1, 2016
https://doi.org/10.4134/JKMS.j140298
Copyright © The Korean Mathematical Society.
S. Reza Moghadasi
Sharif University of Technology
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
MSC numbers: Primary 93B27; Secondary 70E18, 93B05, 70Q05
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