The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed in such systems. We derive how the semi-major axis evolves in these cases. We analyze two astrophysically interesting examples, those of the harmonic and quadrupole perturbations.

Barnabás Deme

Celestial Mechanics and Dynamical Astronomy

国际期刊 CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY 关注天体力学及其应用的广泛主题，以及周边领域。发表在《天体力学和动力天文学》上的论文包括对行星理论、月球理论、一般和特殊摄动理论、星历表、共振理论、地球和行星的大地测量学、动力学、3-体问题、N体问题、空间力学、环系统、银河动力学、参考系、时间、相对论、非引力、计算机方法、用于分析开发的计算机语言和数据库管理。天体力学和动力天文学是该领域的记录期刊，是动力天文学、天体动力学和动力系统参考图书馆不可或缺的组成部分。

Celestial Mechanics and Dynamical Astronomy is an international journal that focuses on a wide range of topics in celestial mechanics and its applications, as well as related fields. The journal publishes papers covering planetary theory, lunar theory, general and special perturbation theory, ephemerides, resonance theory, geodesy of the Earth and planets, dynamics, the three-body problem, N-body problem, celestial mechanics, ring systems, galactic dynamics, reference frames, time, relativity, non-gravitational effects, computational methods, and computer languages and database management used for analysis and development. Celestial Mechanics and Dynamical Astronomy serves as a vital record journal in the field and is an indispensable resource for dynamical astronomy, celestial dynamics, and dynamical systems research.

《Celestial Mechanics and Dynamical Astronomy》是一本国际期刊，专注于天体力学及其应用的广泛主题，以及相关领域的研究。该期刊发表的论文涵盖了行星理论、月球理论、一般和特殊摄动理论、星历表、共振理论、地球和行星的大地测量学、动力学、三体问题、N体问题、空间力学、环系统、银河动力学、参考系、时间、相对论、非引力效应、计算机方法，以及用于分析和开发的计算机语言和数据库管理等内容。《Celestial Mechanics and Dynamical Astronomy》是该领域的重要记录期刊，是动力天文学、天体动力学和动力系统研究的不可或缺的参考资料。

Category	Quartile
物理与天体物理	3
物理与天体物理, 天文与天体物理	3
物理与天体物理, 数学跨学科应用	3

Lagrange’s planetary equations with time-dependent secular perturbations

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Journal Info

Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	3