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The rolling ball problem on the sphere. (English) Zbl 1292.58010

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

Citations:

Zbl 1266.53014
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