The rolling ball problem on the sphere
Biscolla, Laura M. O. (Universidade São Judas Tadeu (São Paulo, Brasil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Oliva, Waldyr M. (Instituto de Matemática e Estatístic. Departamento de Matematica Aplicada)

Date:	2012
Abstract:	By a sequence of rolling motions without slipping or twisting along arcs of maximal circles outside the surface of a sphere of radius R, 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. Assuming R > 1 we provide a new and shorter prove of the result of Frenkel and Garcia in [4] that with at most 4 moves we can go from a given initial state to an arbitrary final state. Important cases such as the so called elimination of the spin discrepancy are done with 3 moves only.
Grants:	European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments/Ajudes: The third author thanks to FCT (Portugal) for the partial support through Program POCTI/FEDER and PDCT/MAT/56476/2004; and thanks also M.V.P. Garcia for many valuable discussions on the subject.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Control theory ; Rolling ball problem
Published in:	Sao Paulo Journal of Mathematics Sciences, Vol. 6 Núm. 2 (2012) , p. 1-9, ISSN 1982-6907

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