A FOURTH-ORDER SOLUTION OF THE IDEAL RESONANCE PROBLEM

被引：2

作者：

Erdi, Balint ^{[1
]}

Kovacs, Jozsef ^{[2
]}

机构：

[1] Eotvos Lorand Univ, Dept Astron, Budapest, Hungary

[2] Eotvos Lorand Univ, Gothard Observ, Szombathely, Hungary

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 1993年 / 56卷 / 1-2期

关键词：

Hamiltonian systems; resonance;

D O I：

10.1007/BF00699734

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a 'Kepler-equation'. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians.

引用

页码：221 / 230

页数：10

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