A remark concerning a mechanical characterization of the sphere
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- Proc. Amer. Math. Soc. 96 (1986), 648-650 Request permission
Abstract:
It is shown that if a (sufficiently) small ball rolls freely without sliding on a compact surface in such a way that its center moves with constant in magnitude velocity for every initial condition, then the surface must be a sphere.References
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F. Noether, Ueber die rollende Bewegung einer Kugel auf Rotationsflächen, Dissertation, München, 1909.
J. I. Neimark and N. A. Fufaev, Dynamics of nonholonomic systems, Transl. Math. Monos., vol. 33, Amer. Math. Soc., Providence, R.I., 1972.
- Barrett O’Neill, Elementary differential geometry, Academic Press, New York-London, 1966. MR 0203595
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 648-650
- MSC: Primary 53A17; Secondary 53A05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826496-1
- MathSciNet review: 826496