  Methodology is developed that incorporates the radiation reaction force into
the relativistic molecular dynamics framework implemented in the MBN Explorer
software package. The force leads to a gradual decrease in the projectile's
energy E due to the radiation emission. This effect is especially strong for
ultra-relativistic projectiles passing through oriented crystals where they
experience the action of strong electrostatic fields as has been shown in
recent experiments. A case study has been carried out for the initial
approbation of the methodology developed. Simulations of the processes of
planar channeling and photon emission have been performed for 150 GeV positrons
in a 200 microns thick single oriented Si(110) crystal. Several regimes for the
decrease in E have been established and characterized. Further steps in
developing the code to include the necessary quantum corrections are identified
and possible algorithmic modifications are proposed.
