  Analytic solution of semiclassical dynamics equations of the Dicke model in a
superradiant state is presented. The time dependences of the amplitudes of
superradiant bosonic condensate and coherent two-level atomic array in the
microwave cavity prove to be expressed via Jacobi elliptic functions of real
time and manifest existence of an adiabatic invariant of motion in the strongly
coupled system. The periodic beatings of the photonic and atomic coherent state
amplitudes are shifted in time revealing an effect of 'bound luminosity', when
energy stored in the two-level system during 'darkness' in the cavity is
suddenly converted into photonic condensate that 'illuminates' the cavity for
half a period, before it plunges into 'darkness' again.
