The purpose of this work is to determine the location and stability of the Cassini states of a celestial body with an inviscid fluid core surrounded by a perfectly rigid mantle. Both situations where the rotation speed is either non-resonant or trapped in a $$p\!:\!1$$ p : 1 spin–orbit resonance where p is a half integer are addressed. The rotation dynamics is described by the Poincaré–Hough model which assumes a simple motion of the core. The problem is written in a non-canonical Hamiltonian formalism. The secular evolution is obtained without any truncation in obliquity, eccentricity or inclination. The condition for the body to be in a Cassini state is written as a set of two equations whose unknowns are the mantle obliquity and the tilt angle of the core spin axis. Solving the system with Mercury’s physical and orbital parameters leads to a maximum of 16 different equilibrium configurations, half of them being spectrally stable. In most of these solutions, the core is highly tilted with respect to the mantle. The model is also applied to Io and the Moon.

中文翻译：

---

具有液体核心的刚体的卡西尼状态

这项工作的目的是确定一个天体的卡西尼状态的位置和稳定性，该天体具有一个被完美刚性地幔包围的无粘性流体核心。解决了旋转速度为非共振或陷入 $$p\!:\!1$$p 的两种情况：1 自旋轨道共振，其中 p 是半整数。旋转动力学由 Poincaré-Hough 模型描述，该模型假设核心的简单运动。这个问题是用非规范的哈密顿形式主义写成的。长期演变是在没有任何倾斜、偏心率或倾斜度截断的情况下获得的。天体处于卡西尼状态的条件被写成一组两个方程，其未知数是地幔倾角和核心自旋轴的倾斜角。使用水星的物理和轨道参数求解系统会导致最多 16 种不同的平衡配置，其中一半在光谱上是稳定的。在大多数这些解决方案中，地核相对于地幔高度倾斜。该模型也适用于 Io 和月球。