Kinetic energy transformation

Please let me know a reference where the transformation of the kinetic energy is performed.
Thanks

 

kinetic energy

Thanks. There is a poblem. K is a physical quantity for which we do not define a proper value whereas for E we do.

 

Thanks. For a less sophisticated audience I would present the problem as:
Start with the expression of the kinetic energy in I
K=mcc[(1/g(u))-1] (1)
where g(u) stands for gamma as a function of the speed of the bullet in I,
Express the right side of (1) as a function of u' the speed of the bullet in I' via the composition law of parallel speeds in order to obtain
K=mcc[(1+u'V/cc)/g(V)g(u'))-1] (2)
The transformation equation (2) leads to the following consequences
a. For u'=0
K=mcc[(1/g(V))-1)
b.For V=0 (u'=u)
K=mcc[(1/g(u))-1]
whereas for u'=0 and V=0
K=0
all in good accordance with phyhsical reality!
Is there some thing wrong in my derivation?
Use please soft words and hard arguments:rofl: