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Summary:
The equations of variation with respect to the straight-lineequilibrium points $L_1,L_2,L_3$ of the elliptic three-dimensional restricted problem of three bodies are equivalent to a system of two differential equations of the second order and one Hill's equation. In the paper presented here, this Hill's equation is studied and a proof is given that this differential equation has no nontrivial periodic solution.
References:
[1] Г. H. Дубошин: Небесная механика, Аналитические и качественные методы. Издательство Наука, Москва, 1964. Zbl 1117.65300
[2] H. Hochstadt: Differential Equations, A Modern Approach. Holt, Rinehart and Winston, New York, Chicago, San Francisco, Toronto, London, 1964. MR 0209536 | Zbl 0128.30501
[3] A. Kufner J. Kadlec: Fourier Series. Academia, Prague, 1971. MR 0393989
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