An invariant region for the collisional dynamics of two bodies on Keplerian orbits

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• 作者：Dario Benedetto ; Flavia Lenti
• 关键词：Planetary systems ; Planetary rings ; Elastic collisions ; Inelastic collisions
• 刊名：Bollettino dell'Unione Matematica Italiana
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：9
• 期：4
• 页码：513-525
• 全文大小：
• 刊物类别：Mathematics, general;
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：2198-2759
• 卷排序：9

文摘

We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable values of the total energy and the total angular momentum (explicitly computable) the orbits of the bodies remain elliptic, whatever are the number and the details of the collisions. The invariant region exists also in the case of two bodies interacting by short range potential.