INVESTIGATION OF TWO FIXED CENTERS PROBLEM AND HENON-HEILES POTENTIAL BASED ON THE POINCARE SECTION - Malkov Ewgenii,; Bekov Askar,; Momynov Serzhan,; Beckmuhamedov Ilias.,; Kurmangaliev Duman,; Mukametzhan Aidana,; Orynqul Iltefat, (Academic Scientific Journal of Computer Science, 2019)
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 HenonHeiles 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     1 the internal cross-sectional structure decomposes from the values H  1.7, but the internal cross-sectional structure is preserved in the interval H   [ 0.5, 1.6], in the case 1   0.9 and 2   0.1 the internal cross-sectional structure decomposes from the values H  0.9 but the internal cross-sectional structure is preserved in the interval H   [ 0.3, 0.8] , in the case of 1   0.7 and 2   0.3 the internal cross-sectional structure decomposes from the values H  0.8, but the internal cross-sectional structure is preserved in the interval H   [ 0.2, 0.7] . 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.