Excuse me ... .

In non-relativistic mechanics, the Galilean transformation will yield the Galilean velocity addition formula ... , whereas ... , in the special theory of relativity, the Lorentz’s transformation of space-time will yield the Einstein’s velocity addition formula ... . The Einstein’s velocity addition formula, which reduce to Galilean velocity addition formula if the magnitude of the velocities are much smaller than (speed of light in vacuum) ... .

If the velocity of particle and are and , respectively, relative to observer , and the velocity of observer is relative to observer , then

- the velocity of relative to is , and

- the velocity of relative to is ,

where ... .

If we want such that , we will get an equation

,

which has three components because the equation is 3-vector equation ... .

We are asked to find alias from the vector equation (alias three scalar component equations) ... .

Does there exist other methods to find from three simultaneous non-linear scalar equation which containing ... ?

Does the solution for of this vector equation must be numerical solution ... ? Does there exist an analytical solution of ... ?

Thank you very much ... .