The rolling ball problem on the plane revisited

Biscolla, Laura M. O. [UNESP]; Llibre, Jaume; Oliva, Waldyr M.

The rolling ball problem on the plane revisited

Data

2013-08-01

Autores

Biscolla, Laura M. O.

Llibre, Jaume

Oliva, Waldyr M.

Editor

Springer

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

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.