Some remarks on flows of line elements and frames

doi:10.1007/978-3-642-01742-1_13

Part of the book series: Vladimir I. Arnold - Collected Works ((ARNOLD,volume 1))

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Abstract

It is well known that many problems in mechanics can be reduced to geodesic flows (see [1-4]). In this note we define more general dynamic systems in the spaces of line elements and frames of a Riemannian manifold - the isotropic flows. These include flows connected with curves of constant geodesic curvature and with the motion of a charged particle on a smooth surface in the presence of a magnetic field.

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Editors and Affiliations

Department of Mathematics, University of California, 94720-3840, Berkeley, CA, USA
Alexander B. Givental
Department of Mathematics, University of Toronto, M5S 3G3, Toronto, ON, Canada
Boris A. Khesin
Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, 91125-8100, Pasadena, CA, USA
Jerrold E. Marsden
Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA
Alexander N. Varchenko
Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russian Federation
Oleg Ya. Viro
Institute of Mathematical Sciences, Stony Brook University, 11794-3660, Stony Brook, NY, USA
Vladimir M. Zakalyukin

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(2009). Some remarks on flows of line elements and frames. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_13

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DOI: https://doi.org/10.1007/978-3-642-01742-1_13
Publisher Name: Springer, Berlin, Heidelberg
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