I've been trying to derive the velocity addition rule for vectors. For the moment I'm just considering 2 spatial dimensions. The results I'm getting look rather nasty. For example, I got(adsbygoogle = window.adsbygoogle || []).push({});

[tex]w_x=\frac{u_x+v_x+\frac{u_y}{u^2}(u_xv_y-u_yv_x)(1-\frac 1 \gamma)}{1+u_xv_x+u_yv_y}[/tex]

Does anyone have the correct answer? My result has the correct behavior in the limit [itex]c\rightarrow\infty[/itex], but I still think it looks weird.

(The gamma is the one corresponding to u, not v, and when I write "u" without an index, that's the magnitude of the vector).

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# Vector addition of velocities

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