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Classical Solutions for a Perturbed N-Body System

  • Conference paper
Topological Nonlinear Analysis II

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 27))

Abstract

In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses m 1,…m N , described in cartesian coordinates

$$ x_1,...x_N,\,x_k \in R^3 \,x_k \equiv \{ x_k,1,\,x_k,2,\,x_k,3\} $$

by the system of equations

$$ m_k \ddot x_k = g\,\sum\limits_{1 \leqslant i < k \leqslant N} {\frac{{m_i m_k }}{{\left| {x_i - x_k } \right|^3 }}(x_k - x_i ) + \nabla _k w(x,t)} $$
((0.1))

where

$$ \nabla _{k,m} \equiv \frac{\partial }{{\partial x_{k.m} }},\,m = 1,2,3. $$

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Authors and Affiliations

  1. Dip. di Matematica, Univ. Roma, La Sapienza Laboratorio Interdisciplinare, SISSA, Trieste, Italy

    Gianfausto Dell’ Antonio

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  1. Gianfausto Dell’ Antonio
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Editors and Affiliations

  1. Department of Mathematics, University of Rome, Tor Vergata, 00133, Rome, Italy

    Michele Matzeu  & Alfonso Vignoli  & 

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© 1997 Birkhäuser Boston

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Antonio, G.D. (1997). Classical Solutions for a Perturbed N-Body System. In: Matzeu, M., Vignoli, A. (eds) Topological Nonlinear Analysis II. Progress in Nonlinear Differential Equations and Their Applications, vol 27. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4126-3_1

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  • DOI: https://doi.org/10.1007/978-1-4612-4126-3_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8665-3

  • Online ISBN: 978-1-4612-4126-3

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