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

Vassilis S. Kalantonis (), Angela E. Perdiou () and Christos N. Douskos ()
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Vassilis S. Kalantonis: University of Patras
Angela E. Perdiou: University of Patras
Christos N. Douskos: University of Patras

A chapter in Applications of Nonlinear Analysis, 2018, pp 523-535 from Springer

Abstract: 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.

Keywords: Asymptotic Orbits; Lyapunov Periodic Orbits; Collinear Equilibrium Points; Homoclinic Orbit; Classical Hill Problem (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-89815-5_18

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