We examine a 2-DOF Hamiltonian system modeling some previously unexplored dynamical effects in first-order mean motion resonances in the spatial circular restricted three-body problem “star-planet-asteroid.” In distinction from the well-known integrable model of Sessin and Ferraz-Mello (Celest Mech Dyn Astron 32:307–332, 1984) and Wisdom (Celest Mech Dyn Astron 38:175–180, 1986), in our analysis, we kept more terms in the expansion for the disturbing function. This allowed us to study the phenomena caused by coexisting resonant modes, that were lost in the integrable model. In addition, we identified the areas of dynamical chaos in the phase space of the considered system. Despite the non-integrability of our model, we were able to compute analytically many quantities characterizing its dynamical behavior. Finally, we illustrate some of our results through the examples of the known resonant Kuiper belt objects.

中文翻译：

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具有共存共振模式的平均运动共振中长期动力学的可分析处理模型

我们研究了一个 2-DOF 哈密顿系统，该系统对空间圆形受限三体问题“星-行星-小行星”中的一阶平均运动共振中的一些先前未探索的动力学效应进行建模。与著名的 Sessin 和 Ferraz-Mello (Celest Mech Dyn Astron 32:307–332, 1984) 和 Wisdom (Celest Mech Dyn Astron 38:175–180, 1986) 的可积模型不同，在我们的分析中，我们保留了干扰函数的扩展中的更多项。这使我们能够研究由可积模型中丢失的共存谐振模式引起的现象。此外，我们确定了所考虑系统的相空间中的动态混沌区域。尽管我们的模型具有不可积性，但我们能够通过分析计算表征其动力学行为的许多数量。最后，