Based on the Timoshenko beam theory, a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton’s principle and Euler angles. The associated conventional model is provided for comparison purpose. The features of the proposed mathematical model are discussed based on some selected coordinate systems. The frequencies and modes are investigated to show the influences of centrifugal terms on the stability of the gyroscopic systems. The results show that the novel model proposed may lose stability due to the centrifugal terms. It is also found that the backward precession mode can be changed into a forward one beyond the critical rotating velocity.

中文翻译：

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基于Timoshenko梁理论的挠性转子建模与稳定性分析

基于蒂莫申科梁理论，利用汉密尔顿原理和欧拉角，建立了具有离心项的旋转轴数学模型。提供相关的常规模型用于比较目的。基于一些选定的坐标系，讨论了所提出的数学模型的特征。研究了频率和模式，以显示离心项对陀螺系统稳定性的影响。结果表明，所提出的新模型可能由于离心项而失去稳定性。还发现后退进动模式可以改变为超过临界转速的前进模式。