Bookmark 7: Free motion of the Dirac particle with a constant CM velocity
v
z
=0.1 along OZ axis, and the CM spin orientation is θ=60∘ and ϕ=200∘. We see the zitter motion of the CC (dotted blue in the right plot) and the CM trajectory (dotted red). Attached to these points it is drawn the comoving Cartesian frames. It is also depicted the Center of Mass spin
S
CM
(red) and the Center of Charge spin
S
(blue). On the right picture both spins are depicted to see that the
S
CM
is conserved but
S
is not, as given in (23) because the spin dynamics

S
t
=
P

u
, is orthogonal to the constant linear momentum along the velocity
v
, and
S
precesses around
S
CM
direction.The two components of the angular velocity
ω
p
and
ω
u
(magenta), are also drawn. The component
ω
u
has the opposite direction to the velocity of the CC,
u
, because the angle α between the vector
ω
p
and the velocity
v
is α>π/2, formula (36). If α<π/2,
ω
u
is in the same direction than the CC velocity
u
(see Bookmark 8). This component of the angular velocity is different from zero to produce the torsion of the CC trajectory and vanishes when this trajectory is flat.