Hyperbolic motion (relativity)

Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram.

The proper acceleration of a particle is defined as the acceleration that a particle "feels" as it accelerates from one inertial reference frame to another. This can be derived mathematically as

where is the instantaneous speed of the particle, is the speed of light, and is time. Solving for the equation of motion results in

which is a hyperbola in time and the spatial location variable

Hyperbolic motion is easily visualized on a Minkowski diagram, where the motion of the accelerating particle is along the -axis. Each hyperbola is defined by

See also

References

External links

This article is issued from Wikipedia - version of the 11/7/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.