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The non-resonant secular dynamics of compact planetary systems are modeled bya perturbing function which is usually expanded in eccentricity and absoluteinclination with respect to the invariant plane. Here, the expressions aregiven in a vectorial form which naturally leads to an expansion in eccentricityand mutual inclination. The two approaches are equivalent in most cases, butthe vectorial one is specially designed for those where a quasi-coplanar systemtilts as a whole by a large amount. Moreover, the vectorial expressions of theHamiltonian and of the equations of motion are slightly simpler than thosegiven in terms of the usual elliptical elements. We also provide the secularperturbing function in vectorial form expanded in semimajor axis ratio allowingfor arbitrary eccentricities and inclinations. The interaction between theequatorial bulge of a central star and its planets is also provided, as is therelativistic periapse precession of any planet induced by the central star. Weillustrate the use of this representation for following the secularoscillations of the terrestrial planets of the solar system, and for Kozaicycles as may take place in exoplanetary systems.

Compact planetary systems perturbed by an inclined companion: I. Vectorial representation of the secular model