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

## Авторы

• E.A. Malkov Khristianovich Institute of Theoretical and Applied Mechanics Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
• A.A. Bekov Al-Farabi Kazakh National University, Almaty, Kazakhstan
• S.B. Momynov Satbayev University, Almaty, Kazakhstan
• I.B. Beckmuhamedov Al-Farabi Kazakh National University, Almaty, Kazakhstan
• D.M. Kurmangaliyev Al-Farabi Kazakh National University, Almaty, Kazakhstan
• A.M. Mukametzhan Al-Farabi Kazakh National University, Almaty, Kazakhstan
• I.S. Orynqul MSOE «Almaty College of Fashion and Design», Almaty, Kazakhstan

## Ключевые слова:

Henon-Heiles model, the problem of two fixed centers, Poincaré section, numerical solutions.

## Аннотация

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 121μμ== the internal cross-sectional structure decomposes from the values 1.7H=−, but the internal cross-sectional structure is preserved in the interval [0.5,1.6]H∈−−, in the case 10.9μ=and 20.1μ= the internal cross-sectional structure decomposes from the values 0.9H=− but the internal cross-sectional structure is preserved in the interval [0.3,0.8]H∈−−, in the case of 10.7μ= and 20.3μ= the internal cross-sectional structure decomposes from the values 0.8H=−, but the internal cross-sectional structure is preserved in the interval [0.2,0.7]H∈−−. 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.

2020-02-04

## Как цитировать

Malkov, E., Bekov, A., Momynov, S., Beckmuhamedov, I., Kurmangaliyev, D., Mukametzhan, A., & Orynqul, I. (2020). INVESTIGATION OF TWO FIXED CENTERS PROBLEM AND HENON-HEILES POTENTIAL BASED ON THE POINCARE SECTION. Известия НАН РК. Серия физико-математическая, (1), 55–61. извлечено от https://journals.nauka-nanrk.kz/physics-mathematics/article/view/392

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