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 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.