Accelerated motion and special relativity transformations

Abstract

Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity vector as three additional coordinates to time and geometric coordinates is studied. Turns in pseudoplane (dt,dv) of this 7-space describe accelerated motion of frame. In addition to the light velocity, the transformation formulas contain a fundamental constant which has a meaning of maximal acceleration. It is demonstrated that if a source of light moves with acceleration with respect to some reference frame, the light velocity in this frame is less than the constant $c$ and depends on acceleration. The special relativity relation between energy, impulse, and mass gets changed for particle in accelerated motion. A generalized wave operator being invariant to the above transformations is introduced. The components of tensor and of potential of electromagnetic field get intermixing in transformation relations for accelerated frame.