Displaying similar documents to “Bar Billiards and Poncelet’s Porism”

An example of a non-degenerate precession possessing two distinct pairs of axes

Giancarlo Cantarelli, Corrado Risito (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the present paper we provide an interesting example of a non-degenerate precession possessing two distinct pairs p , f , p ′ , f ′ of axes of precession and figure. Thus the problem arises of the existence of classes of precessions possessing a unique axis of precession and a unique axis of figure. In the fourth section we show that the class of non-degenerate regular precessions enjoys this property.

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Constantin Călin, Mircea Crasmareanu (2014)

Czechoslovak Mathematical Journal

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We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant...