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Thread: The Einsteinís Velocity Addition

  1. #1 The Einsteinís Velocity Addition 
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    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 ... .


    Last edited by trfrm; March 18th, 2013 at 01:08 PM.
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  3. #2  
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    Quote Originally Posted by trfrm View Post
    Excuse me ... .

    Thank you very much ... .
    This sounds very much like a homework problem. The Forum's homework policy is to help, but not to do. So, please tell us what you've done so far to solve it, and where you've gotten stuck. Someone here will give you some hints so that you can solve it yourself.


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  4. #3  
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    Oh ... . I’m sorry very much ... . Really, this problem is not a homework problem ... . I just want know the brief clue of alternative solution to solve the equation ... . I just know that

    • ,



    • ,



    • , and



    • ,


    in Cartesian coordinate system ... .

    Maybe ... , its analytic solution does not exist ... . If in special case (one-dimension), , , and ... , then the vector equation becomes

    ,

    alias ,

    alias ,

    alias ,

    alias ... .

    alias ... .

    But ... , this is a special case in one-dimension, not 3-dimension ... .
    Last edited by trfrm; March 19th, 2013 at 05:11 AM.
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