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

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 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.