Invariant tori in the secular motions of the three-body planetary systems

被引：42
|
作者：
Locatelli, U [1 ]
Giorgilli, A [1 ]
机构：
[1] Dipartimento Matemat, I-20133 Milan, Italy
来源：
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2000年 / 78卷 / 1-4期
关键词：
KAM theory; stability in planetary motion; three-body problem; computer-assisted proofs;
D O I：
10.1023/A:1011139523256
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun-Jupiter-Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.
引用
收藏
页码：47 / 74
页数：28
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