  The equations of in-medium gluodynamics are proposed. Their classical lowest
order solution is explicitly shown for a color charge moving with constant
speed. For nuclear permittivity larger than 1 it describes emission of
Cherenkov gluons resembling results of classical electrodynamics. The choice of
nuclear permittivity and Lorentz-invariance of the problem are discussed.
Effects induced by the transversely and longitudinally moving (relative to the
collision axis) partons at LHC energies are described.
