The rolling ball problem on the plane revisited

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

doi:https://doi.org/10.1007/s00033-012-0279-8

The rolling ball problem on the plane revisited

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

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 language	English
Pages (from-to)	991-1003
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	64
Issue number	4
DOIs	https://doi.org/10.1007/s00033-012-0279-8
Publication status	Published - 1 Aug 2013

Keywords

Control theory
Hammersley problem
Kendall problem
Rolling ball

Access to Document

https://doi.org/10.1007/s00033-012-0279-8

ddd.uab.cat Link

Fingerprint Dive into the research topics of 'The rolling ball problem on the plane revisited'. Together they form a unique fingerprint.

Cite this

@article{32094aa2dc5f4829978a2525c1b55555,

title = "The rolling ball problem on the plane revisited",

abstract = "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. {\textcopyright} 2012 Springer Basel.",

keywords = "Control theory, Hammersley problem, Kendall problem, Rolling ball",

author = "Biscolla, {Laura M.O.} and Jaume Llibre and Oliva, {Waldyr M.}",

year = "2013",

month = aug,

day = "1",

doi = "https://doi.org/10.1007/s00033-012-0279-8",

language = "English",

volume = "64",

pages = "991--1003",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - The rolling ball problem on the plane revisited

AU - Biscolla, Laura M.O.

AU - Llibre, Jaume

AU - Oliva, Waldyr M.

PY - 2013/8/1

Y1 - 2013/8/1

N2 - 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.

AB - 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.

KW - Control theory

KW - Hammersley problem

KW - Kendall problem

KW - Rolling ball

UR - https://ddd.uab.cat/record/150656

U2 - https://doi.org/10.1007/s00033-012-0279-8

DO - https://doi.org/10.1007/s00033-012-0279-8

M3 - Article

VL - 64

SP - 991

EP - 1003

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 4

ER -