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It is shown that the Nachtmann boosting method of introducing coordinates onde Siter manifolds can be completed with suitable gauge transformations able tokeep under control the transformation under isometries of the conservedquantities. With this method, the rest local charts (or natural frames) aredefined pointing out the role of the conserved quantities in investigating therelative geodesic motion. The advantages of this approach can be seen from theapplications presented here. For the first time, the simple kinematic effects,the electromagnetic field of a free falling charge and the binary fission aresolved in terms of conserved quantities on the expanding portion of the deSitter spacetime.

Rest frames and relativistic effects on de Sitter spacetimes