INVESTIGATION OF TWO FIXED CENTERS PROBLEM AND HENON-HEILES POTENTIAL BASED ON THE POINCARE SECTION

E. A. Malkov, A. A. Bekov, S.B. Momynov, I.B. Beckmuhamedov, D.M. Kurmangaliyev, A.M. Mukametzhan, I.S. Orynqul

2020

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DOI 10.32014/2020.2518-1726.7
Data confidence 70 medium
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Abstract

In this paper, we study the Henon-Heiles potential and the problem of two fixed centers.In studies of nonlinear systems for which exact solutions are unknown, the Poincare section method is used.For the Henon-Heiles potential, Poincare sections were obtained.Next, the potential of two fixed centers was investigated.It was shown on the basis of the Poincare section that, in the case 1 2. With increasing energy, many of these surfaces decay.It is assumed that the numerical results obtained will serve as the basis for comparison with analytical solutions.