  We advance an universal approach to the construction of kinematics in
non-inertial and, in particular, rotating reference frames. On its basis a
10-dimensional space including three projections of velocity vector and three
turn angles in geometric space as additional coordinates to time and geometric
coordinates is introduced. In a specific case, the turns in 10-space describe
the uniform rotation of reference frame as well as its accelerated motion.
Transformations for coordinates and angular velocities are derived. Definitions
of dynamic quantities contain a fundamental constant $\Omega$ with
dimensionality of angular velocity and the maximal acceleration in addition to
the velocity of light. The special relativity relation between energy, impulse,
and mass gets changed for particles with moment of inertia. A wave equation
obtained describes the rotary and accelerated motions of light wave. A relation
between particle moment and the Planck constant representing Bohr's postulate
is added to de Broglie's relations. A generalized space-time which allows to
consider kinematics for derivations of arbitrary order is studied. Differential
relations between velocity of arbitrary order and turn angles in the
generalized space-time are obtained.
