1203.0754 (Vitaliy V. Voytik)
Vitaliy V. Voytik
With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found transformation of velocity from the laboratory system S to an arbitrary rigid progressively moving reference frame s. Set the physical meaning of the parameter $\mathbf{v}(t)$ in the appropriate LMN transformation. For small distances, and their proper smooth motion without jerks suggested the reverse 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 frame s in the frame S. The applicability of the reverse 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 velocity S in the comoving but not rotating frame of s. It is shown that when the local non-inertial motion a rigidly rotating frame of reference kinematic strain relative to the laboratory frame of reference is not in the two planes. The application of this transformation to a rotating rigid body is discussed. The angle of proper rotation when the Wigner boost is calculated. We find differential equations for the inverse problem of relativistic kinematics, and their decision in the case of uniformly accelerated motion. There are two ways to show the inapplicability of usual mechanical solution for uniformly accelerated motion. The mutual compensation of their proper Thomas precession and proper Wigner rotation is shown. Also, the basic formulas are expressed in terms of the parameter $\mathbf {v'}(t)$, which is solution of the equation for the inverse problem of relativistic kinematics.
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http://arxiv.org/abs/1203.0754
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