  With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found
transformation of velocity from the laboratory system S to an accelerated,
rotating frame of reference s. The physical sense of parameter entering into
the LMN special transformation is established. For small distances, and their
proper smooth motion without jerks suggested the inverse special LMN
transformation. The main consequences of this transformation is considered,
namely, a) the desync in moving frame of reference s of proper clocks of the
pre-synchronized in the laboratory frame S and b) the Lorentz contraction of
proper rulers of frame s in the frame S. The applicability of the inverse LMN
transformation for real frames with maximum rigidity is established. Equations
for the rotation matrix is obtained. It is shown that the intrinsic rotation of
the axes s, considered with respect to S is not rigid. Found the direct and
inverse transformation of affine "angular" velocity in the S to the comoving,
but not rotating frame s. Also shown that for the non-inertial motion of
rigidly rotating frame of reference her the kinematic deformation of
coordinates system is absent in two planes. The application of this
transformation to a rotating rigid body is considered. The matrice and angle of
proper Wigner rotation is calculated. We find differential equations for the
inverse problem of relativistic kinematics, and their decision in the case of
uniformly accelerated motion. The close connection between the proper Thomas
precession and the proper Wigner rotation and their mutual compensation for the
case uniformly accelerated motion has shown. The difference of the uniformly
accelerated motion from the hyperbolic one has been shown. Also, the basic
formulas are expressed in terms of the parameter, which is solution of the
equation for the inverse problem of relativistic kinematics.
