Abstract
The effect of small perturbing forces in the relative dynamics of trial particles is studied. An asymptotic approximation is obtained for the solution of the problem with accuracy to withinɛ 2 in the nonresonant case and in the case of the fundamental and off-multiple resonances. Phenomena associated with nonlinear resonance (a cutoff of the oscillation amplitude and parametric resonance) arise in the system.
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L. E. Piragas, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 74 (1978).
K. A. Piragas, V. I. Zhdanov, A. N. Aleksandrov, and L. E. Piragas, “A nonlinear effect for motion in a field with mirror symmetry,” Abstracts of Papers at the All-Union Conference on Modern Theoretical and Experimental Problems in the Theory of Relativity and Gravity [in Russian], Minsk (1976).
L. D. Landau and E. M. Lifshitz, Mechanics, Vol. 1, Pergamon.
N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 21–30, December, 1978.
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Piragas, L.E. Nonlinear effects in the relative dynamics of trial particles in the general theory of relativity II. Effect of small perturbing forces. Soviet Physics Journal 21, 1540–1546 (1978). https://doi.org/10.1007/BF00892466
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DOI: https://doi.org/10.1007/BF00892466