The rolling ball problem on the plane revisited

Laura M.O. Biscolla, Jaume Llibre, Waldyr M. Oliva

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


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 2π. © 2012 Springer Basel.
Original languageEnglish
Pages (from-to)991-1003
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number4
Publication statusPublished - 1 Aug 2013


  • Control theory
  • Hammersley problem
  • Kendall problem
  • Rolling ball


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