Rapidity - Wikipedia

In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that ... Rapidity FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Measureofrelativisticvelocity Inrelativity,rapidityiscommonlyusedasameasureforrelativisticvelocity.Mathematically,rapiditycanbedefinedasthehyperbolicanglethatdifferentiatestwoframesofreferenceinrelativemotion,eachframebeingassociatedwithdistanceandtimecoordinates. Forone-dimensionalmotion,rapiditiesareadditivewhereasvelocitiesmustbecombinedbyEinstein'svelocity-additionformula.Forlowspeeds,rapidityandvelocityareproportionalbut,forhighervelocities,rapiditytakesalargervalue,withtherapidityoflightbeinginfinite. Usingtheinversehyperbolicfunctionartanh,therapiditywcorrespondingtovelocityvisw=artanh(v/c)wherecisthevelocityoflight.Forlowspeeds,wisapproximatelyv/c.Sinceinrelativityanyvelocityvisconstrainedtotheinterval−c