Non-Null Lie Quadratics in E3

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    Abstract

    Interpolation problems in the space SO(3) of rotations of Euclidean 3-space E3 are reviewed in Secs. I s2 as background and motivation to a study of curves in E3 called Lie quadratics. Except for a special class called null, Lie quadratics have resisted analysis until now. The rest of the present paper is devoted to new results showing non-null Lie quadratics have rich analytical, geometrical, and asymptotic structures: rates of growth are studied using differential equations and inequalities, Lie quadratics are proved to be extendible over the whole of , and existence of axes is proved under fairly general conditions. Examples show sharpness of many results.
    Original languageEnglish
    Pages (from-to)4334-4351
    JournalJournal of Mathematical Physics
    Volume45
    Issue number11
    DOIs
    Publication statusPublished - 2004

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