Biscolla, Laura M. O.; Llibre, Jaume; Oliva, Waldyr M. The rolling ball problem on the sphere. (English) Zbl 1292.58010 São Paulo J. Math. Sci. 6, No. 2, 145-154 (2012). Summary: By a sequence of rolling motions without slipping or twisting along arcs of great 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 L. M. Frenkel and M. V. P. Garcia [Qual. Theory Dyn. Syst. 10, No. 2, 333–341 (2011; Zbl 1266.53014)] 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. MSC: 58E25 Applications of variational problems to control theory 93B27 Geometric methods 70B10 Kinematics of a rigid body 70E18 Motion of a rigid body in contact with a solid surface 53A17 Differential geometric aspects in kinematics Keywords:control theory; rolling ball problem Citations:Zbl 1266.53014 PDFBibTeX XMLCite \textit{L. M. O. Biscolla} et al., São Paulo J. Math. Sci. 6, No. 2, 145--154 (2012; Zbl 1292.58010) Full Text: DOI