Reference frames in classical and relativistic physics

Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated or rotating frames. A conception of the system of coordinates associated with a reference frame is introduced. It is shown that one of these coordinates can be regarded as temporal coordinate, and the others as spatial ones. It is demonstrated that in relativistic case nondiagonal spatial-temporal components of the metric tensor are always equal to zero. Inertial, accelerated, and rotating reference frames are considered as examples.