Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi-periodic cycles via re-inversing of the proper ultra-elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

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关于卫星准周期轨道的潮汐演化

众所周知，行星与其卫星之间的潮汐相互作用是决定卫星轨道演化的主要现象。土星潮汐耗散理论中的现代 ansatz 先前是由来自各个国家的天体力学领域的国际科学家团队开发的。我们对潮汐耗散理论的应用涉及对控制卫星轨道演化的 ODE 方程（常微分方程）系统的研究；这种由2个常微分方程组成的极其非线性的系统描述了轨道偏心的相互内部动力学以及将适当卫星的半长轴纳入这样一个可怕的方程。在我们的推导中，我们已经为上述系统提出了优雅的分析解决方案；因此，我们 ansatz 的动机是将先前提出的方程组转换为方便的形式，其中需要最少的数值计算来获得最终解。最好是解析解；我们通过对适当的超椭圆积分进行反演，将解决方案呈现为一组准周期循环。它意味着偏心率、卫星轨道半长轴演化的准周期特征以及地球潮汐耗散的准周期特征。其中需要最少的数值计算来获得最终解。最好是解析解；我们通过对适当的超椭圆积分进行反演，将解决方案呈现为一组准周期循环。它意味着偏心率、卫星轨道半长轴演化的准周期特征以及地球潮汐耗散的准周期特征。其中需要最少的数值计算来获得最终解。最好是解析解；我们通过对适当的超椭圆积分进行反演，将解决方案呈现为一组准周期循环。它意味着偏心率、卫星轨道半长轴演化的准周期特征以及地球潮汐耗散的准周期特征。