Let us now return to the specific system dealt with in this thesis; i.e. a set of
particles i (galaxies) of mass 
, expressed in comoving coordinates 
(see equation (2.5)) in an expanding universe with a mean mass density
. The goal of this section is to determine the equations of motion for these
particles using Hamilton's principle from the previous section, but first, we need an
expression for the scalar function 
, the Lagrangian.