Some analytical results about periodic orbits in the restricted three body problem with dissipation

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• 作者：Alessandro Margheri (1) margheri@ptmat.fc.ul.pt
  Rafael Ortega (2) rortega@ugr.es
  Carlota Rebelo (1) carlota@ptmat.fc.ul.pt
• 关键词：Restricted problem &#8211 ; Dissipative forces &#8211 ; Periodic orbits &#8211 ; Fredholm alternative &#8211 ; Hopf bifurcation &#8211 ; Drag
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版年：2012
• 出版时间：July 2012
• 年：2012
• 卷：113
• 期：3
• 页码：279-290
• 全文大小：196.1 KB
• 参考文献：1. Ambrosetti A., Prodi G.: A Primer in Nonlinear Analysis. Cambridge University Press, Cambridge (1993)
  2. Celletti A., Stefanelli L., Lega E., Froeschl茅 C.: Some results on the global dynamics of the regularized restricted three-body problem with dissipation. Celest. Mech. Dyn. Astron. 109, 265–284 (2011)
  3. Hadjidemetriou J.D., Voyatzis G.: On the dynamics of extrasolar planetary systems under dissipation: migration of planets. Celest. Mech. Dyn. Astron. 107, 3–19 (2010)
  4. Hahn W.: Stability of motions. Springer Verlag, Berlin (1967)
  5. Jacobi C.: Jacobi’s Lectures on Dynamics. Hindustan Book Agency, New Delhi (2009)
  6. P谩stor P., Klačka J., K贸mar L.: Motion of dust in mean motion resonances with planets. Celest. Mech. Dyn. Astron. 103, 343–364 (2009)
  7. Pollard H.: Mathematical Introduction to Celestial Mechanics. Prentice Hall, Englewood Cliffs (1966)
  8. Siegel C., Moser J.: Lectures on Celestial Mechanics. Springer, Berlin (1971)
• 作者单位：1. Fac. Ci锚ncias da Univ. de Lisboa e Centro de Matem谩tica e Aplica莽玫es Fundamentais, Campo Grande, Edif铆cio C6, piso 2, 1749-016 Lisboa, Portugal2. Departamento de Matem谩tica Aplicada, Universidad de Granada, 18071 Granada, Spain
• ISSN：1572-9478

文摘

We present some analytical results about the existence of periodic orbits for the planar restricted three body problem with dissipation considered recently by Celletti et al. (CMDA 109, 265, 2011) We show that, under fairly general conditions on the dissipation term, the circular orbits cannot be continued to the dissipative framework. Moreover, we give general conditions for the occurrence or not of a Hopf bifurcation around the libration points L ₄ and L ₅. Our results are consistent with the numerical findings of Celletti et al.