Dynamics of Kepler problem with linear drag

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• 作者：Alessandro Margheri ; Rafael Ortega…
• 关键词：Kepler problem ; Linear drag ; Collision ; Levi ; Civita transformation
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：120
• 期：1
• 页码：19-38
• 全文大小：409 KB
• 参考文献：1. Breiter, S., Jackson, A.: Unified analytical solutions to two-body problems with drag. Mon. Not. R. Astron. Soc. 299, 237-43 (1998) CrossRef
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  14. Zhang, Z.F., Ding, T.R., Huang, W.Z., Dong, Z. X.: Qualitative Theory of differential Equations, Vol. 101 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI. Translated from the Chinese by Anthony Wing Kwok Leung (1992)
  
• 作者单位：Alessandro Margheri (1)
  Rafael Ortega (2)
  Carlota Rebelo (1)
  
  1. Centro de Matemática e Aplica??es Fundamentais, Faculdade de Ciências Universidade de Lisboa, 1749-016?, Lisboa, Portugal
  2. Departamento de Matemática Aplicada, Universidad de Granada, 18071?, Granada, Spain
  
• ISSN：1572-9478

文摘

We study the dynamics of Kepler problem with linear drag. We prove that motions with nonzero angular momentum have no collisions and travel from infinity to the singularity. In the process, the energy takes all real values and the angular velocity becomes unbounded. We also prove that there are two types of linear motions: capture–collision and ejection–collision. The behaviour of solutions at collisions is the same as in the conservative case. Proofs are obtained using the geometric theory of ordinary differential equations and two regularizations for the singularity of Kepler problem equation. The first, already considered in Diacu (Celest Mech Dyn Astron 75:1-5, 1999), is mainly used for the study of the linear motions. The second, the well known Levi-Civita transformation, allows to complete the study of the asymptotic values of the energy and to prove the existence of collision solutions with arbitrary energy.