Asymptotic expansion of the angle between successive maximal distances for a 2-body system with potential

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• 作者：Thomas de Jong ; ^{t.g.d.jong@tue.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Asymptotics expansions ; Bertrand&rsquo ; s theorem ; Perturbed elliptic integrals ; Hamiltonian systems ; Classical mechanics
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：5
• 页码：1107-1115
• 全文大小：243 K

文摘

Based on an example of Arnold (1989, page 37) we perturb the classical Newtonian 2-body problem by considering the potential 23266f2d993c63c2e4bc1d59ba" title="Click to view the MathML source">−1/r^1+ε$-1/r^{1+\epsilon }$ with ε≪1$\epsilon \ll 1$. Restricting to orbits close to circular motion we compute an asymptotic expansion in ε$\epsilon$ of the angle between the successive positions where the distance between the bodies is maximal.