An Euclidean space is quite dominant. An Euclidean space ranges form minus infinity to infinity in 3 direction. A second Euclidean system is a contradiction in termini. The velocity V0 is strange, to which Euclidean system does it belong and why can't it be an acceleration. If we step over the obvious illogic aspects we could start reasoning. Suppose equations 1 en 4 lead to mathematical correct descriptions. Then we have the problem; why should the system 2 result be observed differently in system 1 as both systems have the same Euclidean physical laws for the same phenomena. In relativity all physical laws in Euclidean systems stay valid in their own system to describe the observed facts. The observed facts from system 2 are no observed facts in system 1? But lets step over this problem. If use equation 7 to fill in into equation 6, we get equation 8. To have a result with no parameters from system 2, then we need to replace the t' to. There needs to be relation between t and t'. I have taken equation 11. It is easy to see that a dt'/dt = constant would not lead to different order equations. But the equation 11 leads to higher order equations. The two Euclidean systems constellation leads to higher order equations.
 
 
 
 
 
 
 
 
 
 
Some pictures out of my reasoning
Third order
Third order Third order Third order
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