Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

被引：8

作者：

Maciejewski, Andrzej J. ^{[1
]}

Szuminski, Wojciech ^{[2
]}

Przybylska, Maria ^{[2
]}

机构：

[1] Univ Zielona Gora, Janusz Gil Inst Astron, Licealna 9, PL-65407 Zielona Gora, Poland

[2] Univ Zielona Gora, Inst Phys, Licealna 9, PL-65407 Zielona Gora, Poland

来源：

PHYSICS LETTERS A | 2017年 / 381卷 / 07期

关键词：

Integrability obstructions; Liouville integrability; Morales-Ramis theory; Differential Galois theory; Constant curvature spaces; SPHERE;

D O I：

10.1016/j.physleta.2016.12.030

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous potential in flat spaces. Thanks to this property Hamilton equations admit, in a general case, a particular solution. Using this solution we derive necessary integrability conditions investigating differential Galois group of variational equations. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：725 / 732

页数：8

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