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A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

机译：基于分布质量惯性力的顶级营养数学模型

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The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.
机译：陀螺仪的主要特性是保持旋转转子的轴，这是一个基于角动量变化原理建立的数学模型。该原理用于已知出版物中的顶部运动的数学建模。然而，陀螺仪设备的实际测试并不符合这种分析方法。最近的研究表明，陀螺仪特性的起源比已知出版物中所描述的更为复杂。陀螺仪上施加的扭矩基于多个惯性力的作用产生旋转的转子的内部扭矩。这些力是离心力，科里奥利力和惯性力，以及由旋转转子的质量元素和中心质量产生的角动量的变化。这些扭矩的作用在陀螺仪设备的阻力扭矩和旋进扭矩中表现出来。这些惯性转矩围绕两个轴同时且相互依赖地起作用，代表了陀螺仪理论的基本原理。新的惯性扭矩使得可以推导著名陀螺运动的数学模型，陀螺是陀螺仪设备的最简单形式。这项工作的新颖性是基于围绕其两个轴作用的八种惯性力作用的顶部运动的数学模型。通过机器动力学和振动分析来表示所获得的用于顶部章动和自稳定的数学模型。对于平衡良好的顶部和顶部以及中心质量偏心的运动的新分析方法肯定会响应实际结果。

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