Nonlinear effects in the relative dynamics of trial particles in the general theory of relativity II. Effect of small perturbing forces

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 within² 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.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 21–30, December, 1978.