  The non-resonant secular dynamics of compact planetary systems are modeled by
a perturbing function which is usually expanded in eccentricity and absolute
inclination with respect to the invariant plane. Here, the expressions are
given in a vectorial form which naturally leads to an expansion in eccentricity
and mutual inclination. The two approaches are equivalent in most cases, but
the vectorial one is specially designed for those where a quasi-coplanar system
tilts as a whole by a large amount. Moreover, the vectorial expressions of the
Hamiltonian and of the equations of motion are slightly simpler than those
given in terms of the usual elliptical elements. We also provide the secular
perturbing function in vectorial form expanded in semimajor axis ratio allowing
for arbitrary eccentricities and inclinations. The interaction between the
equatorial bulge of a central star and its planets is also provided, as is the
relativistic periapse precession of any planet induced by the central star. We
illustrate the use of this representation for following the secular
oscillations of the terrestrial planets of the solar system, and for Kozai
cycles as may take place in exoplanetary systems.
