The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational fields. One formula can be derived from the octonion torque, calculating the precessional angular velocity generated by the gyroscopic torque. When the octonion force is equal to zero, it is able to deduce the force equilibrium equation and precession equilibrium equation and so forth. From the force equilibrium equation, one can infer the angular velocity of revolution for the particles. Meanwhile, from the precession equilibrium equation, it is capable of ascertaining the precessional angular velocity induced by the torque derivative, including the angular velocity of Larmor precession. Especially, some ingredients of torque derivative are in direct proportion to the field strengths. The study reveals that the precessional angular velocity induced by the torque derivative is independent of that generated by the torque. The precessional angular velocity, induced by the torque derivative, is relevant to the torque derivative and the spatial dimension of precessional velocity. It will be of great benefit to understanding further the precessional angular velocity of the spin angular momentum.

中文翻译：

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复八元空间中的进动角速度和场强

本文旨在应用八元数来探索电磁场和引力场中几种粒子的进动角速度。一些学者利用八元数来研究电磁场和引力场。可以从八元力矩推导出一个公式，计算陀螺力矩产生的进动角速度。当八元力为零时，可以推导出力平衡方程和进动平衡方程等。从力平衡方程，可以推断出粒子的旋转角速度。同时，根据进动平衡方程，可以确定扭矩导数引起的进动角速度，包括拉莫尔进动角速度。尤其，转矩导数的某些成分与场强成正比。研究表明，扭矩导数引起的进动角速度与扭矩产生的角速度无关。由转矩导数引起的进动角速度与转矩导数和进动速度的空间维度有关。进一步了解自旋角动量的进动角速度将大有裨益。与扭矩导数和进动速度的空间维度有关。进一步了解自旋角动量的进动角速度将大有裨益。与扭矩导数和进动速度的空间维度有关。进一步了解自旋角动量的进动角速度将大有裨益。