Revisiting dynamical orbits in the planar anisotropic Kepler problem

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-02-11 DOI:10.1016/j.ijnonlinmec.2025.105029

Sergey Ershkov

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引用次数: 0

Abstract

In this investigation, a novel solving method has been introduced for determining the coordinates of a mass point m₂ in orbit around a more massive primary m₁ (within the framework of modified version of the restricted two-body problem, R2BP). Such analytical approach describes periodic orbits for the planar anisotropic Kepler problem instead of the classical Kepler's formulation of the R2BP. Simultaneously, a system of equations of motion in polar coordinates has been derived and then successfully explored to identify the quasi-periodic orbits for the planar anisotropic Kepler problem which are proved to be slightly quasi-oscillating along the elliptic classical orbit according to Kepler's law for R2BP. An analytical expression has been obtained for the function of polar radius via elegant procedure of integration (a successful repetitive cascade of changes of appropriate variables). So, solution can be presented via quasi-periodic cycles of oscillations of trajectory of mass point m₂ moving around a massive primary m₁.

MSC classes

70F15, 70F07.

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.