Variational proof of the existence of periodic orbits in the spatial Hill problem and its constrained problems

被引：0

作者：

Iguchi, Shota ^{[1
]}

Kajihara, Yuika ^{[1
]}

Shibayama, Mitsuru ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Sakyo Ku, Yoshida Honmachi, Kyoto 6068501, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2023年 / 40卷 / 01期

关键词：

Hill problem; Periodic orbits; Variational methods;

D O I：

10.1007/s13160-022-00539-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Hill problem models the motion of a particle near a planet. In this paper, we show the existence of symmetric periodic orbits in the spatial Hill problem by using the variational method. We also study the problem under a constraint on a prescribed plane and show the existence of periodic orbits in the problem. The obtained orbits are applicable to artificial satellites around the Earth and other planets.

引用

页码：513 / 524

页数：12

共 10 条

[1] Minimization properties of Hill's orbits and applications to some N-body problems [J].

Arioli, G ;

Gazzola, F ;

Terracini, S .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2000, 17 (05) :617-650

[2]

Chen KC, 2010, AM J MATH, V132, P681

[3] A remarkable periodic solution of the three-body problem in the case of equal masses [J].

Chenciner, A ;

Montgomery, R .

ANNALS OF MATHEMATICS, 2000, 152 (03) :881-901

[4] Families of periodic orbits in Hill's problem with solar radiation pressure: application to Hayabusa 2 [J].

Giancotti, Marco ;

Campagnola, Stefano ;

Tsuda, Yuichi ;

Kawaguchi, Jun'ichiro .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2014, 120 (03) :269-286

[5] Variational existence proof for multiple periodic orbits in the planar circular restricted three-body problem [J].

Kajihara, Yuika ;

Shibayama, Mitsuru .

NONLINEARITY, 2022, 35 (03) :1431-1446

[6] TRANSVERSALITY OF THE INVARIANT-MANIFOLDS ASSOCIATED TO THE LYAPUNOV FAMILY OF PERIODIC-ORBITS NEAR L2 IN THE RESTRICTED 3-BODY PROBLEM [J].

LLIBRE, J ;

MARTINEZ, R ;

SIMO, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1985, 58 (01) :104-156

[7] A variational proof of existence of transit orbits in the restricted three-body problem [J].

Moeckel, R .

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2005, 20 (01) :45-58

[8] Variational Construction of Orbits Realizing Symbolic Sequences in the Planar Sitnikov Problem [J].

Shibayama, Mitsuru .

REGULAR & CHAOTIC DYNAMICS, 2019, 24 (02) :202-211

[9]

Szebehely V., 1967, Theory of Orbits: The Restricted Problem of Three Bodies

[10]

Tonelli L., 1925, B AMERICANMATHEMATIC, V31, P163, DOI 10.1090/S0002-9904-1925-04002-1

← 1 →