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

Thomas Waters, Colin McInnes

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In this paper we consider the orbital dynamics of a solar sail in the Earth-Sun circular restricted 3-body problem. The equations of motion of the sail are given bya set of nonlinear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the sail. We consider first the equilibria and linearisation of the system, then examine the nonlinear 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's 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 pages7
JournalInternational Journal of Non-Linear Mechanics
Publication statusPublished - 2008


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