Abstract
We examine the basic dynamics associated with a simple model of a dust particle interacting with a planetary gravitational field, solar radiation pressure and a constant magnetic field. We find the presence of global equilibrium points that are analogous to the Lagrangian equilibria of the circular restricted three-body problem.
Linear stability analysis is carried out for the equilibrium points in order to establish stability conditions in terms of the two free parameters of the problem. However, linear stability does not ensures Lyapunov stability and further analysis is needed. To go further in the analysis, we apply a theorem due to Arnold that ensures Lyapunov stability almost for every pair of the free parameters but for some resonant cases. These resonant cases are analyzed by studying the phase flow on the reduced phase space after normalization.
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References
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© 2001 Springer Science+Business Media Dordrecht
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Lanchares, V., López-Moratalla, T., Farrelly, D. (2001). Lyapunov Stability for Lagrange Equilibria of Orbiting Dust. In: Pretka-Ziomek, H., Wnuk, E., Seidelmann, P.K., Richardson, D.L. (eds) Dynamics of Natural and Artificial Celestial Bodies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1327-6_32
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DOI: https://doi.org/10.1007/978-94-017-1327-6_32
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5865-2
Online ISBN: 978-94-017-1327-6
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