Abstract
In order to find a law characterising the decrease of velocity along a jet, five analytical methods are suggested. The first two simple models examine the variation of velocity in the presence of Newton's or Stoke's resistance. The equation that represents the conservation of the momentum along a pyramidal sector is solved from an analytical point of view (third model). The application of the conservation of the total momentum flux allows us to deduce the velocity of the galaxy as a function of time for classical velocities (fourth model) and relativistic velocities (fifth model). The variation of velocity along the jet combined with an adequate composition of jet precession velocity, rotational velocity of the galaxy, and galaxy velocity dispersion in the cluster allows us to trace the geometrical pattern of the head-tail radio sources. Application of the developed theory/code to the radio galaxies NGC1265, NGC4061, NGC326, and Cygnus A gives the central galaxy's approximate dispersion velocities in the direction perpendicular to the jet. A transition from head-tails to classical double radio galaxies as a function of the increasing jet's mechanical power is introduced.
