When the transformation equations are required to satisfy the light signal equations in the form " x " = " ct " and " x " 2 = " ct " 2, by substituting the x and x'- values, the same technique produces the same expression for the Lorentz factor.
12.
By plugging these transformation rules into the full Maxwell's equations, it can be seen that if Maxwell's equations are true in one frame, then they are " almost " true in the other, but contain incorrect terms pro by the Lorentz transformation, and the field transformation equations also must be changed, according to the expressions given below.
13.
If the transformation equations defining the generalized coordinates are independent of " t ", and the Lagrangian is a sum of products of functions ( in the generalized coordinates ) which are homogeneous of order 0, 1 or 2, then it can be shown that " H " is equal to the total energy " E " = " T " + " V ".
