  The paper focuses on considering some special precessional motions as the
spin motions, separating the octonion angular momentum of a proton into six
components, elucidating the proton angular momentum in the proton spin puzzle,
especially the proton spin, decomposition, quarks and gluons, and polarization
and so forth. J. C. Maxwell was the first to use the quaternions to study the
electromagnetic fields. Subsequently the complex octonions are utilized to
depict the electromagnetic field, gravitational field, and quantum mechanics
and so forth. In the complex octonion space, the precessional equilibrium
equation infers the angular velocity of precession. The external
electromagnetic strength may induce a new precessional motion, generating a new
term of angular momentum, even if the orbital angular momentum is zero. This
new term of angular momentum can be regarded as the spin angular momentum, and
its angular velocity of precession is different from the angular velocity of
revolution. The study reveals that the angular momentum of the proton must be
separated into more components than ever before. In the proton spin puzzle, the
orbital angular momentum and magnetic dipole moment are independent of each
other, and they should be measured and calculated respectively.
