  By means of numerical methods, we solve the equations of motion for the
collapse of a shell of baryonic matter, made of galaxies and substructure
falling into the central regions of a cluster of galaxies, taking into account
the effect of the dynamical friction. The parameters on which the dynamical
friction mainly depends are: the peaks' height, the number of peaks inside a
protocluster multiplied by the correlation function evaluated at the origin,
the filtering radius and the nucleus radius of the protocluster of galaxies. We
show how the collapse time (Tau) of the shell depends on these parameters. We
give a formula that links the dynamical friction coefficient (Eta) o the
parameters mentioned above and an analytic relation between the collapse time
and (Eta). Finally, we obtain an analytical relation between (Tau) and the mean
overdensity (mean Delta) within the shell. All the analytical relations that we
find are in excellent agreement with the numerical integration.
