  Analytic solution is presented of the nonlinear semiclassical dynamics of
superradiant photonic condensate that arises in the Dicke model of two-level
atoms dipolar coupled to the electromagnetic field in the microwave cavity. In
adiabatic limit with respect to photon degree of freedom the system is
approximately integrable and its evolution is expressed via Jacobi elliptic
functions of real time. Periodic trajectories of the semiclassical coordinate
of photonic condensate either localise around two degenerate minima of the
condensate ground state energy or traverse between them over the saddle point.
An exact mapping of the semiclassical dynamics of photonic condensate on the
motion of unstable Lagrange 'sleeping top' is found. Analytic expression is
presented for the frequency dependence of transmission coefficient along a
transmission line inductively coupled to the resonant cavity with superradiant
condensate. Sharp transmission drops reflect Fourier spectrum of the
semiclassical motion of photonic condensate and of 'sleeping top' nodding.
