THE CRITERION FOR TRANSFERABLE SELF-CONSISTENTLY TRANSLATIONALITY OF COORDINATE TRANSFORM OPERATORS AND REFERENCE FRAMES IN UNIVERSAL KINEMATICS

From an intuitive point of view universal kinematics are collections (sets) of changing objects, which evolve, being in a certain spatial-geometric environment, and evolution of whi- ch can be observed from many different frames of reference. Moreover, the definition of uni- versal kinematics impose the existence of some (preassigned) universal coordinate transform between every two reference frames of such kinematics. Transferable self-consistently translati- onal reference frames (in vector universal kinematics) are interesting because for such reference frames it is possible to give a clear and unambiguous definition of displacement of a moving reference frame relative to a fixed one, which does not depend on the choice of a fixed point in the moving frame of reference. In the present paper it is shown that an arbitrary reference frame m is transferable self-consistently translational relatively to a reference frame l (in some vector uni- versal kinematics F) if and only if the coordinate transform operator from the reference frame m to the reference frame l is transferable self-consistently translational. Therefore transferable self-consistently translational coordinate transform operators describe the conversion of coordi- nates from the moving and transferable self-consistently translational frame of reference to the (given) fixed frame in vector universal kinematics. Also in the paper it is described the structure of transferable self-consistently translational coordinate transform operators (this is the main result of the article). Using this result it have been obtained the necessary and sufficient conditi- on for transferable self-consistently translationality of one reference frame relatively to another in vector universal kinematics.