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, 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 implementation of normal forms, Nekhoroshev-type estimates or KAM theory.
Celletti A., De Blasi I., Di Ruzza S. (2025). Perturbative methods and synchronous resonances in Celestial Mechanics. APPLIED MATHEMATICAL MODELLING, 143 [10.1016/j.apm.2025.116040].
Perturbative methods and synchronous resonances in Celestial Mechanics
Di Ruzza S.
2025-01-01
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, 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 implementation of normal forms, Nekhoroshev-type estimates or KAM theory.
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