Stability of periodic solutions for Hill’s averaged problem with allowance for planetary oblateness |
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| Authors: | M A Vashkov’yak N M Teslenko |
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| Institution: | (1) Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia |
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| Abstract: | We analyze the stability of periodic solutions for Hill’s double-averaged problem by taking into account a central planet’s oblateness. They are generated by steady-state solutions that are stable in the linear approximation. By numerically calculating the monodromy matrix of variational equations, we plot its trace against the integral of the problem—an averaged perturbing function, for two model systems, (Sun + Moon)-Earth-satellite] and (Sun-Uranus-satellite). We roughly estimate the ranges of values for the parameters of satellite orbits corresponding to periodic solutions of the evolutionary system that are stable in the linear approximation. |
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| Keywords: | Hill’ s averaged problem stability satellite orbits |
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