Secondary resonance effects in the spherical motion of a heavy asymmetrical rigid body with moving masses are reviewed in the case close to the Lagrange top. It is known that perturbations acting on the body, particularly a small displacement of the center of mass with respect to axis of symmetry and a small perturbing moment in a connected system of coordinates, lead to non-resonant evolutions of angular velocity. These evolutionary phenomena are called direct secondary resonance effects. They are visible in a dynamic system consisting of an asymmetric rigid body and several masses fixed relative to the body. However, the presence of moving masses connected to a rigid body by springs may lead to the stabilization of the angular velocity of the body. This dynamic phenomenon should be attributed to the inverse secondary resonance effect. The aim of this paper is to study the characteristic direct and inverse secondary resonance effects in a perturbed spherical motion of a rigid body with fixed and moving masses. The method of integral manifolds and the averaging method are used for the asymptotic analysis of the secondary resonance effects. The paper presents the numerical results of modeling the direct and inverse resonance effects.

中文翻译：

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具有移动质量的非对称刚体的球面运动中的正反二次共振效应

在靠近拉格朗日顶的情况下，回顾了具有移动质量的重的非对称刚体的球形运动中的二次共振效应。众所周知，作用在物体上的扰动，特别是质心相对于对称轴的小位移和连接坐标系中的小扰动力矩，会导致角速度的非共振演化。这些进化现象被称为直接二次共振效应。它们在一个由非对称刚体和几个相对于该体固定的质量组成的动态系统中可见。然而，通过弹簧连接到刚体的移动质量的存在可能导致刚体角速度的稳定。这种动态现象应归因于逆二次共振效应。本文的目的是研究具有固定和移动质量的刚体的扰动球面运动中特征性的直接和逆次共振效应。二次共振效应的渐近分析采用积分流形法和平均法。本文介绍了模拟正反共振效应的数值结果。