The classical theory of perturbations and the problem of stability of planetary systems

doi:10.1007/978-3-642-01742-1_18

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

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Abstract

1. The theory of perturbations enables us to predict planetary motion for many years ahead with all necessary accuracy. However, qualitative questions on the behavior of a system during an infinite time interval, for example the problem of stability, could not be solved by the theory of perturbations. Planetary motion is described in this theory by series of the form

$$ \sum_{m,n} a_{mn} \cos[(m \omega_{1} + n \omega_{2})t + \phi_{mn}] $$

.

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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). The classical theory of perturbations and the problem of stability of planetary systems. 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_18

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DOI: https://doi.org/10.1007/978-3-642-01742-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01741-4
Online ISBN: 978-3-642-01742-1
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