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The Rolling of One Curve or Surface Upon Another

1961; Taylor & Francis; Volume: 68; Issue: 4 Linguagem: Inglês

10.1080/00029890.1961.11989669

1930-0972

William Kingdon Clifford, James J. McMahon,

Geometric and Algebraic Topology

It is well known in dynamics [1 ] that any general motion of a lamina in its own plane may be generated by the rolling of one curve upon another. In his book on continuous groups, Kowalewski [2 ] gives a mathematical treatment of this result, and here, by using matrix methods, we shall generalize his theorem to spaces of higher dimensions. The motion of a body in Euclidean space of n dimensions is generated by the transformation