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

About Lorentz-M{\o}ller-Nelson transformation to rigid noninertial frame of reference