If we look the relations of Lorentz Boost; t′=1√1−v2c2(t−vxc2)
we can concentrate on 2D case, and as v=axbt
then we can write; t′=1√1−(axbt)2c2(t−(axbt)xc2)
And these Reduce a bit to; t′=1√1−(axbt)2c2(t−ax2btc2)
Wo when these are combined to v′ then v′=a√1−(axbt)2c2(x−axb)b√1−(axbt)2c2(t−ax2btc2)
Which can be written; v′=a(x−axb)√1−(axbt)2c2√1−(axbt)2c2b(t−ax2btc2)
And this reduces quickly just to; v′=a(x−axb)11b(t−ax2btc2)=a(x−axb)b(t−ax2btc2)
And v′=ax−a2xbbt−bax2btc2=ax−a2xbbt−ax2tc2
So, this would be the Lorentz -Transformation for velocity; v′=ax−a2xbbt−ax2tc2
Question; Are these kind of higher level Lorentz Transformation been properly analysed before? (Source)
1. Velocity
2. Acceleration
3. Jerk
4. Momentum
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