Using the theoretical Ramachandran (phi, psi) maps reported in the literature for sucrose in vacuo and in aqueous solution, we constructed a two-degrees of freedom model in which the glucose and fructose units are substituted by pseudo-atoms. The complete dynamics of this model is studied numerically at fixed energies. Use is made of the graphic method of the Poincaré surfaces of section in phase space and of the Lissajous maps in configuration space. The reduction to just two degrees of freedom allows one to deal with all initial conditions in phase space, whereas the results of molecular dynamics calculations with all internal degrees of freedoms and with the explicit consideration of solvent molecules are taken into account via effective kinetic and potential energy terms. The conformational isomerization mechanism is investigated by singling out the most reactive trajectories in phase space that are associated with the so-called reactive islands and with the resonances found between the phi and psi motions.