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Figure 1
The schematic depicts the stationary ground frame (GF, [ {\bf x}-c{\bf t}]) observer. With respect to the GF, the train frame (TF, [ {\bf x}'-c{\bf t}']) observer moves with a velocity v in the + x direction. With respect to the GF, an event (a bird) frame (BF) moves at a velocity u in the + x direction. The hyperbolic angles ([\alpha] and [\beta]) are defined by the velocities u and v relative to c as indicated, and are illustrated in Fig. 2[link].

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