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Pàgina inicial > Articles > Articles publicats > The rolling ball problem on the plane revisited |
Data: | 2013 |
Resum: | By a sequence of rollings without slipping or twisting along segments of an 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 [3]. His proof is more algebraic than ours which is more geometric. |
Ajuts: | Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Nota: | Agraïments: The third author thanks the FCT (Portugal) for the partial support through Program POCTI/FEDER and PDCT/MAT/56476/2004. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Control theory ; Rolling ball |
Publicat a: | ZAMP. Journal of Applied Mathematics and Physics, Vol. 64 Núm. 4 (2013) , p. 991-1003, ISSN 1420-9039 |
Postprint 10 p, 572.7 KB |