  Assuming equation of state for quintessential matter: $p=w(z)\rho$, we
analyse dynamical behaviour of the scale factor in FRW cosmologies. It is shown
that its dynamics is formally equivalent to that of a classical particle under
the action of 1D potential $V(a)$. It is shown that Hamiltonian method can be
easily implemented to obtain a classification of all cosmological solutions in
the phase space as well as in the configurational space. Examples taken from
modern cosmology illustrate the effectiveness of the presented approach.
Advantages of representing dynamics as a 1D Hamiltonian flow, in the analysis
of acceleration and horizon problems, are presented. The inverse problem of
reconstructing the Hamiltonian dynamics (i.e. potential function) from the
luminosity distance function $d_{L}(z)$ for supernovae is also considered.
