Classical Solutions for a Perturbed N-Body System

  • Gianfausto Dell’ Antonio
Conference paper
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 27)


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
$$ m_k \ddot x_k = g\,\sum\limits_{1 \leqslant i < k \leqslant N} {\frac{{m_i m_k }}{{\left| {x_i - x_k } \right|^3 }}(x_k - x_i ) + \nabla _k w(x,t)} $$
$$ \nabla _{k,m} \equiv \frac{\partial }{{\partial x_{k.m} }},\,m = 1,2,3. $$


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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Gianfausto Dell’ Antonio
    • 1
  1. 1.Dip. di MatematicaUniv. Roma, La Sapienza Laboratorio Interdisciplinare, SISSATriesteItaly

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