  We consider a Randall-Sundrum two-brane cosmological model in the low energy
gradient expansion approximation by Kanno and Soda. It is a scalar-tensor
theory with a specific coupling function and a specific potential. Upon
introducing the FLRW metric and perfect fluid matter on both branes in the
Jordan frame, the effective dynamical equation for the the A-brane (our
Universe) scale factor decouples from the scalar field and B-brane matter
leaving only a non-vanishing integration constant (the dark radiation term). We
find exact solutions for the A-brane scale factor for four types of matter:
cosmological constant, radiation, dust, and cosmological constant plus
radiation. We perform a complementary analysis of the dynamics of the scalar
field (radion) using phase space methods and examine convergence towards the
limit of general relativity. In particular, we find that radion stabilizes at a
certain finite value for suitable negative matter densities on the B-brane.
Observational constraints from Solar system experiments (PPN) and primordial
nucleosynthesis (BBN) are also briefly discussed.
