This paper by Robert A. Nelson derives an exact, explicit coordinate transformation between an inertial frame of reference and a frame of reference having an arbitrary time-dependent, nongravitational acceleration and an arbitrary time-dependent angular velocity. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000028000010002379000001 The sophisticated formalism of this article is beyond my mathematical training. I would like to study a simplified, non-rotating, 1+1-dimensional version of the transformation. Can it be written out for someone at the undergraduate level? What is the exact, explicit coordinate transformation between an inertial frame of reference and an arbitrarily accelerated frame of reference for one spatial dimension?