Formation of the composite photonic-excitonic particles, known as polaritons,
is an emerging phenomenon in materials possessing strong coupling to light. The
organic-based materials besides the strong light-matter interaction also
demonstrate strong interaction of electronic and vibrational degrees of
freedom. We utilize the Dirac-Frenkel variation principle to derive
semiclassical equations for the vibration-assisted polariton wavefunction
evolution when both types of interactions are treated as equally strong. By
means of the approach, we study details of the polariton relaxation process and
the mechanism of the polariton light emission. In particular, we propose the
photon emission mechanism, which is realized when the polariton wave package
exceeds the geometrical size of the nanosystem. To verify our conclusions we
reproduce the fluorescence peak observed in experiment (Takazawa
\textit{et.al.} Phys.Rev.Let. \textbf{105}:07401, 2010) and estimate the
light-matter interaction parameter