Landau classical field theory question

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SUMMARY

In the discussion regarding Landau's classical field theory, specifically on page 24 of the 4th edition, the derivation of the relativistic equation of motion for a uniformly accelerated particle is analyzed. The key steps involve the transformation of differentials, where Landau equates du to dv in both frames and utilizes the relationship ds = (1/gamma) * cdt. This approach leads to the formulation of the differential equation necessary for deriving the relativistic motion result.

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One page 24 of his book on classical field theory (4th edition), Landau derives the relativistic equation of motion for a uniformly accelarated particle. How does he get the differential equation that leads him to his result?
 
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I assume it is as follows. He took du=dv in both frames, then said ds=1/gamma * cdt. But that still boters me.
 

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