Bifurcation near Boundaries of Regions of Stability of Libration Points in the Three-Body Problem

被引：3

作者：

Yumagulov, M. G. ^{[1
]}

Belikova, O. N. ^{[2
]}

Isanbaeva, N. R. ^{[1
]}

机构：

[1] Bashkir State Univ, Ufa, Russia

[2] Bashkir State Univ, Sibai Inst Branch, Sibai, Russia

来源：

ASTRONOMY REPORTS | 2018年 / 62卷 / 02期

关键词：

ELLIPTIC-RESTRICTED PROBLEM; TRIANGULAR POINTS; 3; BODIES; SYSTEMS;

D O I：

10.1134/S1063772918020075

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

The construction of regions of stability in a linear approximation for the triangular libration points in the planar, elliptical, restricted three-body problem is considered, together with the main scenarios for bifurcation when the parameters of the system pass through a boundary of such a region. A new scheme for constructing the boundaries of regions of stability is proposed, which leads to approximate formulas describing these boundaries. The resonance properties of the boundary points (from the point of view of the theory of local bifurcations) are studied. It is shown that one of the main scenarios for bifurcation is the appearance of non-stationary, 4 pi-periodic solutions close to a triangular libration point.

引用

页码：144 / 153

页数：10

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