Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits

Thomas J. Waters, Colin R. McInnes

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18 Citations (Scopus)
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In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the previous term We consider first the equilibria and linearisation of the system, then examine the non-linear system paying particular attention to its periodic solutions and invariant manifolds. Interestingly, we find there are equilibria admitting homoclinic paths where the stable and unstable invariant manifolds are identical. What is more, we find that periodic orbits about these equilibria also admit homoclinic paths; in fact the entire unstable invariant manifold winds off the periodic orbit, only to wind back onto it in the future. This unexpected result shows that periodic orbits may inherit the homoclinic nature of the point about which they are described.
Original languageEnglish
Pages (from-to)490-496
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Issue number6
Publication statusPublished - Jul 2008


  • solar sail
  • homoclinic
  • periodic orbit
  • three-body problem


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