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Asymptotic Orbits in Hill’s Problem When the Larger Primary is a Source of Radiation

In: Applications of Nonlinear Analysis

Author

Listed:
  • Vassilis S. Kalantonis

    (University of Patras)

  • Angela E. Perdiou

    (University of Patras)

  • Christos N. Douskos

    (University of Patras)

Abstract

A modification of the Hill problem when the larger primary is a source of radiation is considered and asymptotic motions around the collinear equilibrium points are studied. Our work focuses on the computation of homoclinic orbits to the collinear equilibrium points themselves or to the Lyapunov orbits emanating from each equilibrium point. These orbits depart asymptotically from an equilibrium point (or a Lyapunov orbit) and return to the same point (or orbit) asymptotically. In both cases, semi-analytical solutions have been obtained in order to determine appropriate initial conditions which have been used as suitable seed for the numerical computation of the asymptotic orbits with a predetermined accuracy. In addition, for homoclinic orbits to the Lyapunov periodic orbits, transversality is achieved by the construction of appropriate surface of section portraits of the unstable manifolds.

Suggested Citation

  • Vassilis S. Kalantonis & Angela E. Perdiou & Christos N. Douskos, 2018. "Asymptotic Orbits in Hill’s Problem When the Larger Primary is a Source of Radiation," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 523-535, Springer.
  • Handle: RePEc:spr:spochp:978-3-319-89815-5_18
    DOI: 10.1007/978-3-319-89815-5_18
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    Cited by:

    1. Abdullah A. Ansari & Sawsan Alhowaity & Elbaz I. Abouelmagd & Shiv K. Sahdev, 2022. "Analysis of Equilibrium Points in Quantized Hill System," Mathematics, MDPI, vol. 10(13), pages 1-12, June.

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