Abstract
After investigating the two-dipole problem (first generalization of Stormer–s problem of one magnetic dipole), we proceed one step further along the same lines by setting and investigating the three-dipole problem. Each of the three magnetic dipoles is assumed to be located on one member of a three- star system that performs newtonian motions- Charged particles, positive or negative, moving in the vicinity of the three moving dipoles perform motions which are the object of this study. In this paper we show that if the three stars perform the Lagrangean circular solution of the three-body problem and if the magnetic moments of their dipoles are perpendicular to their plane of motion, then three, or two, or one, closed space inside which charged particles of appropriate energy are permanently trapped. These spaces of trappings can be considered as generalized Van Allen zones.
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References
De Vogelaere, R.: 1949, Proc. Sec. Math. Congress, Vancouver, 170–171.
De Vogelaere, R.: 1950, Can. J. Math., 2. 440.
De Vogelaere, R.: 1958, @Contribution to the Theory o-f Non- Linear Oscillations@, Vol. IV, 53–84.
Goudas, C.L. and Petsagourakis, E.G.: 1985, in @Stability of the Solar System and Minor Natural and Artificial Bodies, V. Szebehely (ed.), D. Reidel Publ. Co., Dordrecht, Holland, pp. 349–364.
Goudas, C.L., Leftaki, M. and Petsagourakis, E.G.S 1985a, Celestial Mechanics, 37 127–148.
Goudas, C.L., Leftaki, M. and Petsagourakis, E.G.: 1986, Celestial Mechanics, 39, 57–65.
Goudas, C.L., Leftaki, M. and Petsagourakis, E.G.: 1990, Celestial Mechanics, 47, 1–14.
Graef, C. and Kusaka, S.: 1938, J. Math. Phys., 17,43.
Mavraganis, A.G. and Goudas, C.L.: 1975, Astrophys. Sp. Sci., 32, 115.
Mavraganis, A.G.: 1979, Astrophys. Sp. Sci., 80, 130–133.
Mavraganis, A.G. and Pangalos, C.A.: 1983, Indian J. pure appl.Math., 14(3), 297–306
Stormer, C.F.: 1907, Arch. Sci. Phys. et Nat. Geneve, 24, 350.
Stormer, C.F.: 1955, @Polar Aurora@, Oxford University Press, Oxford, England.
Van Allen, J.: 1958, J. Geophys. Res., 64, 11, 1683.
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© 1991 Plenum Press, New York
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Goudas, C.L., Petsagourakis, E.G. (1991). The Three-Dipole Problem. In: Roy, A.E. (eds) Predictability, Stability, and Chaos in N-Body Dynamical Systems. NATO ASI Series, vol 272. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5997-5_30
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DOI: https://doi.org/10.1007/978-1-4684-5997-5_30
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