Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force

被引：0
作者：
Shibayama, Mitsuru [1 ]
Yamada, Junji [1 ]
机构：
[1] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Sakyo Ku, Yoshida Honmachi, Kyoto 6068501, Japan
来源：
REGULAR & CHAOTIC DYNAMICS | 2021年 / 26卷 / 04期
关键词：
nonintegrability; three-body problem; HAMILTONIAN-SYSTEMS; MEROMORPHIC NONINTEGRABILITY; 1ST INTEGRALS; NONEXISTENCE; INTEGRABILITY;
D O I：
10.1134/S1560354721040079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the planar three-body problem with generalized potentials. Some nonintegrability results for these systems have been obtained by analyzing the variational equations along homothetic solutions. But we cannot apply it to several exceptional cases. For example, in the case of inverse-square potentials, the variational equations along homothetic solutions are solvable. We obtain sufficient conditions for nonintegrability for these exceptional cases by focusing on some particular solutions that are different from homothetic solutions.
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收藏
页码：439 / 455
页数：17
相关论文
共 26 条
  • [1] Acosta-Humanez P, 2008, DISCRETE CONT DYN-B, V10, P265
  • [2] NON-INTEGRABILITY CRITERIUM FOR NORMAL VARIATIONAL EQUATIONS AROUND AN INTEGRABLE SUBSYSTEM AND AN EXAMPLE: THE WILBERFORCE SPRING-PENDULUM
    Acosta-Humanez, Primitivo B.
    Alvarez-Ramirez, Martha
    Blazquez-Sanz, David
    Delgado, Joaquin
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (03) : 965 - 986
  • [3] The three-body problem and equivariant Riemannian geometry
    Alvarez-Ramirez, M.
    Garcia, A.
    Melendez, J.
    Reyes-Victoria, J. G.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (08)
  • [4] [Anonymous], 1993, New Methods of Celestial Mechanics
  • [5] Arnold V.I, 1989, MATH METHODS CLASSIC, Vsecond, DOI 10.1007/978-1-4757-2063-1
  • [6] Boucher D., 2003, IRMA LECT MATH THEOR, V3, P163
  • [7] Bruns H., 1887, ACTA MATH, V11, P25, DOI DOI 10.1007/BF02612319
  • [8] Crespo T., 2011, ALGEBRAIC GROUPS DIF, DOI [10.1090/gsm/122, DOI 10.1090/GSM/122]
  • [9] INTEGRABILITY OF HAMILTONIAN SYSTEMS WITH HOMOGENEOUS POTENTIALS OF DEGREES ±2. AN APPLICATION OF HIGHER ORDER VARIATIONAL EQUATIONS
    Duval, Guillaume
    Maciejewski, Andrzej J.
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (11) : 4589 - 4615
  • [10] Kimura T., 1969, FUNKC EKVACIOJ-SER I, V12, P269
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