Some studies on Lorentz transformation matrix in non-cartesian co-ordinate system

Abstract

The Lorentz matrices for transformation of co-ordinates in Cartesian system are presented for the cases when the relative velocity between two reference frames is along X , Y and Z axes. The general form of the matrix for transformation of co-ordinates from unprimed to primed frame has been deduced in case of Cartesian co-ordinate system with the help of the above matrices. This matrix has not been transformed to the cases of cylindrical and spherical polar co-ordinates due to the fact that the calculations are cumbersome and lengthy. Hence, considering the relative velocity between two frames along a co-ordinate axis the transformation matrix has been found out for cylindrical and spherical co-ordinates.