We discuss Maxwell's ring model with a quasi-homogeneous potential of the dominant mass, and specially study the vertical libration of Maxwell's ring configuration with a Manev potential. There are two kinds of periodic vertical libration, which are non-alternating and alternating cases. The Hamiltonian is highly symmetric and can be reduced to a simple form with two degrees of freedom. Then the Hamiltonian is expanded near the planar circular relative equilibria. By the Lie transformation technique, the birkhoff norm form up to the fourth order is calculated. When the mass ratio between the ring and the dominant mass, and the coefficient of the second term in a Manev potential are both small enough, the nonlinear stability for the vertical libration of Maxwell's ring configuration with a Manev potential is then proved according to Arnold's stability theorem.

Xingbo Xu

Journal of Nonlinear Mathematical Physics

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS (JNMP) 以 LETTERS、ARTICLES 和 REVIEW ARTICLES 的形式发表关于数学物理中基础数学和计算方法的研究论文。JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 是一本数学期刊，致力于发表与非线性问题在物理和数学中的描述、解决方案和应用。主要科目有：-数学物理非线性方程组-量子代数和可积性-离散可积系统和离散几何-李群理论和李代数的应用-非交换几何-超几何和超可积系统-可积性和不可积性，PAINLEVE分析-逆散射法-孤子方程的几何与扭量理论的应用-经典与量子多体问题-变形与几何量化-INSTANTON, MONOPOLES AND GAUGE THEORY-微分几何与数学物理

The Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers in the form of letters, articles, and review articles on fundamental mathematics and computational methods in mathematical physics. This journal focuses on the description, solutions, and applications of nonlinear problems in both physics and mathematics. The main subjects include: nonlinear equations in mathematical physics, quantum algebra and integrability, discrete integrable systems and discrete geometry, applications of Lie group theory and Lie algebras, noncommutative geometry, hypergeometric and superintegrable systems, integrability and non-integrability (Painlevé analysis), inverse scattering method, geometry of soliton equations and applications of twistors, classical and quantum many-body problems, deformation and geometric quantization, instantons, monopoles, and gauge theory, as well as differential geometry and mathematical physics.

《Journal of Nonlinear Mathematical Physics》 (JNMP) 以信件、文章和综述文章的形式发表关于数学物理中基础数学和计算方法的研究论文。该期刊专注于非线性问题在物理和数学中的描述、解决方案和应用。主要研究领域包括：非线性方程组的数学物理、量子代数与可积性、离散可积系统与离散几何、李群理论与李代数的应用、非交换几何、超几何与超可积系统、可积性与不可积性（Painlevé分析）、逆散射法、孤子方程的几何与扭量理论的应用、经典与量子多体问题、变形与几何量化、瞬子、单极子与规范理论、微分几何与数学物理。

Category	Quartile
物理与天体物理	4
物理与天体物理, 应用数学	4
物理与天体物理, 物理数学物理	4

On the Vertical Libration of Maxwell’s Ring Configuration with a Manev Potential

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