%A Malkov, E.A.
%A Bekov, A.A.
%A Momynov, S.B.
%A Beckmuhamedov, I.B.
%A Kurmangaliyev, D.M.
%A Mukametzhan, A.M.
%A Orynqul, I.S.
%D 2020
%T Poincare sections for two fixed centers problem and Henon-Heiles potential
%K
%X 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. At low energies, the Henon-Heiles system looks integrable, since independently of the initial conditions, the trajectories obtained with the help of numerical integration lie on two-dimensional surfaces, i.e. as if there existed a second independent integral. Next, the potential of two fixed centers was investigated. It was shown on the basis of the Poincare section that, in the case μ 1 = μ 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 , in the case μ 1 = 0.9 and μ 1 = 0.1 the internal cross-sectional structure decomposes from the values but the internal cross-sectional structure is preserved in the interval , in the case of μ 1 = 0.7 and μ 1 = 0.3 the internal cross-sectional structure decomposes from the values , but the internal cross-sectional structure is preserved in the interval . 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.
%U https://bph.kaznu.kz/index.php/zhuzhu/article/view/1239
%J Recent Contributions to Physics (Rec.Contr.Phys.)
%0 Journal Article
%R 10.26577/RCPh.2020.v72.i1.01
%P 4-10%V 72
%N 1
%@ 2663-2276
%8 2020-03-26