Perturbative methods and synchronous resonances in Celestial Mechanics

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2025-02-27 DOI:10.1016/j.apm.2025.116040

Alessandra Celletti , Irene De Blasi , Sara Di Ruzza

引用次数: 0

Abstract

We study the stability of some model problems in Celestial Mechanics, focusing on the dynamics around synchronous resonances, namely 1:1 commensurabilities among the main characteristic frequencies. In particular, we illustrate the following examples: the Earth's satellites dynamics, co-orbital asteroids, the rotational dynamics. Within such model problems we analyze, respectively, the stability of the Zeipel-Lidov-Kozai integral, the triangular Lagrangian points, the spin-orbit resonance. Stability results are obtained through perturbative methods, precisely the implementation of normal forms, Nekhoroshev-type estimates or KAM theory.

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.