Publication: The rolling ball problem on the plane revisited
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Coadvisor
Graduate program
Undergraduate course
Journal Title
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Volume Title
Publisher
Springer
Type
Article
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Acesso restrito
Abstract
By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.
Description
Keywords
Control theory, Rolling ball, Kendall problem, Hammersley problem
Language
English
Citation
Zeitschrift Fur Angewandte Mathematik Und Physik. Basel: Springer Basel Ag, v. 64, n. 4, p. 991-1003, 2013.
