  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.
