6533b820fe1ef96bd127917e
RESEARCH PRODUCT
Positioning systems in Minkowski space-time: Bifurcation problem and observational data
Bartolomé CollJuan Antonio Morales-lladosaJoan Josep Ferrandosubject
PhysicsNuclear and High Energy PhysicsCosmology and Nongalactic Astrophysics (astro-ph.CO)Inertial frame of referenceLog-polar coordinatesCoordinate systemFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)Action-angle coordinatesGeneral Relativity and Quantum CosmologyClassical mechanicsGeneralized coordinatesOrthogonal coordinatesMinkowski spaceAstrophysics - Cosmology and Nongalactic AstrophysicsBipolar coordinatesdescription
In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-10-15 | Physical Review D |