Abstract
Solar sails are a proposed form of spacecraft propulsion using large membrane mirrors to propel a satellite taking advantage of the solar radiation pressure. To model the dynamics of a solar sail we have considered the Earth–Sun Restricted Three Body Problem including the Solar radiation pressure (RTBPS). This model has a 2D surface of equilibrium points parametrised by the two angles that define the sail orientation. In this paper we study the non-linear dynamics close to an equilibrium point, with special interest in the bounded motion. We focus on the region of equilibria close to SL 1, a collinear equilibrium point that lies between the Earth and the Sun when the sail is perpendicular to the Sun–sail direction. For different fixed sail orientations we find families of planar, vertical and Halo-type orbits. We have also computed the centre manifold around different equilibria and used it to describe the quasi-periodic motion around them. We also show how the geometry of the phase space varies with the sail orientation. These kind of studies can be very useful for future mission applications.
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References
Bookless, J., McInnes, C.R.: Control of Lagrange point orbits using solar sail propulsion. In: Proceedings of the 56th International Astronautical Congress (2005)
Carr J.: Applications of Centre Manifold Theory. Springer, New York (1981)
Crawford J.D.: Introduction to bifurcation theory. Rev. Modern Phys. 64, 991–1037 (1991)
Devaney R.L.: Reversible diffeomorphisms and flows. Trans. Am. Math. Soc. 218, 89–113 (1976)
Farrés A., Farrés A.: Dynamical system approach for the station keeping of a solar sail. J. Astronaut. Sci. 58, 199–230 (2008a)
Farrés A., Farrés A.: Solar sail surfing along families of equilibrium points. Acta Atronaut. 63, 249–257 (2008b)
Farrés, A., Jorba, À.: On the high order approximation of the centre manifold for ODEs. preprint (2009)
Gulobitski M., Schaeffer D.G., Stewart I.N.: Singularities and Groups in Bifurcation Theory. Springer, New York (1985)
Jorba À.: A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems. Exp. Math. 8, 155–195 (1999)
Lamb J.S.W., Roberts J.A.G.: Time-reversal symmetry in dynamical systems: a survey. Phys. D Nonlinear Phenom. 112, 1–39 (1998)
Lisano, M.: Solar sail transfer trajectory design and station keeping control for missions to Sub-L1 equilibrium region. In: Proceedings of the 15th AAS/AIAA Space Flight Mechanics Conference. Colorado (2005)
Macdonald, M., McInnes, C.R.: A near-term road map for solar sailing. In: Proceedings of the 55th International Astronautical Congress, Vancouver (2004)
McInnes, A.: Strategies for Solar Sail Mission Design in the Circular Restricted Three-Body Problem, Master Thesis. Purdue University (2000)
McInnes C.R.: Solar Sailing: Technology, Dynamics and Mission Applications. Springer-Praxis, London (1999)
McInnes C.R., McDonald A.J.C., Simmons J.F.L., MacDonald E.W.: Solar sail parking in restricted three-body system. J. Guid. Control Dyn. 17, 399–406 (1994)
Meyer K.R., Hall G.R.: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Springer, New York (1991)
Moser J.K.: On the generalization of a theorem of A. Liapounoff. Comm. Pure Appl. Math. 11, 257–271 (1958)
Rios-Reyes, L., Scheeres, D.J.: Robust solar sail trajectory control for large pre-launch modelling errors. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2005)
Sevryuk M.B.: Reversible Systems. Springer, Berlin (1986)
Sevryuk M.B.: The finite-dimensional reversible KAM theory. Physica D Nonlinear Phenomena 112, 132–147 (1998)
Sijbrand, J.: Properties of the centre manifold. Trans. Am. Math. Soc. 289, 431–469 (1985)
Simó, C.: Analytical and numerical approximation of invariant manifolds. In: Froeschlé, C., Benest, D. (eds.) Les méthodes modernes de la Mecánique Céleste, pp. 285–329. Editions Frontières, Gif-sur-Yvette (1990)
Stoer J., Bulirsch B.: Introduction to Numerical Analysis. Springer, New York (2002)
Szebehely V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967)
Vanderbauwhede, A.: Centre manifolds, normal forms and elementary bifurcations. In: Dynamics Reported. A Series in Dynamical Systems and their Applications, vol. 2 , John Wiley & Sons Ltd (1989)
Waters T.J., McInnes C.R.: Periodic orbits above the ecliptic plane in the solar sail restricted 3-body problem. J. Guid. Control Dyn. 30, 786–793 (2007)
Waters, T.J., McInnes, C.R.: Invariant manifolds and orbit control in the solar sail 3-body problem. J. Guid. Control Dyn. 31, 554–562 (2008)
Yen, C.W.: Solar sail geostorm warning mission design. In: Proceedings of the 14th AAS/AIAA Space Flight Mechanics Conference. Hawaii (2004)
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Farrés, A., Jorba, À. Periodic and quasi-periodic motions of a solar sail close to SL 1 in the Earth–Sun system. Celest Mech Dyn Astr 107, 233–253 (2010). https://doi.org/10.1007/s10569-010-9268-4
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DOI: https://doi.org/10.1007/s10569-010-9268-4