The motion of a rigid body about a fixed point in a homogeneous gravitational field is investigated. The body is not dynamically symmetric and its center of gravity lies on the perpendicular, raised from the fixed point, to one of the circular sections of an ellipsoid of inertia. A body with such mass geometry may precess regularly about a nonvertical axis (Grioli’s precession). The problem of the orbital stability of this precession is solved for critical cases of second-order resonance, when terms higher than degree four in the series expansion of the Hamiltonian of the perturbed motion should be taken into account.

中文翻译：

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非对称陀螺仪在二阶共振下的规则进动的稳定性

研究了均质重力场中刚体绕固定点的运动。物体不是动态对称的，其重心位于从固定点垂直到惯性椭球的圆形部分之一的垂直线上。具有这种质量几何形状的物体可以绕非垂直轴规律地进动（Grioli的进动）。当应考虑扰动运动的哈密顿量级数展开时高于四阶的项时，对于二阶共振的临界情况，解决了该进动的轨道稳定性问题。