Regular and chaotic solutions of the Sitnikov problem near the 3/2 commensurability

被引：20

作者：

Jalali, MA ^{[1
]}

Pourtakdoust, SH ^{[1
]}

机构：

[1] Sharif Univ Technol, Dept Engn Mech, Div Appl Mech, Tehran, Iran

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 1997年 / 68卷 / 02期

关键词：

Sitnikov's problem; periodic motion; resonances; chaotic behavior;

D O I：

10.1023/A:1008216128436

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

Regular solutions at the 3/2 commensurability are investigated for Sitnikov's problem. Utilizing a rotating coordinate system and the averaging method, approximate analytical equations are obtained for the Poincare sections by means of Jacobian elliptic functions and 3 pi-periodic solutions are generated explicitly. It is revealed that the system exhibits heteroclinic orbits to saddle points. It is also shown that chaotic region emerging from the destroyed invariant tori, can easily be seen for certain eccentricities. The procedure of the current study provides reliable answers for the long-time behavior of the system near resonances.

引用

页码：151 / 162

页数：12

共 16 条

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