  The science operations of the LISA Pathfinder mission has demonstrated the
feasibility of sub-femto-g free-fall of macroscopic test masses necessary to
build a LISA-like gravitational wave observatory in space. While the main focus
of interest, i.e. the optical axis or the $x$-axis, has been extensively
studied, it is also of interest to evaluate the stability of the spacecraft
with respect to all the other degrees of freedom. The current paper is
dedicated to such a study, with a focus set on an exhaustive and quantitative
evaluation of the imperfections and dynamical effects that impact the stability
with respect to its local geodesic. A model of the complete closed-loop system
provides a comprehensive understanding of each part of the in-loop coordinates
spectra. As will be presented, this model gives very good agreements with LISA
Pathfinder flight data. It allows one to identify the physical noise source at
the origin and the physical phenomena underlying the couplings. From this, the
performances of the stability of the spacecraft, with respect to its geodesic,
are extracted as a function of frequency. Close to $1 mHz$, the stability of
the spacecraft on the $X_{SC}$, $Y_{SC}$ and $Z_{SC}$ degrees of freedom is
shown to be of the order of $5.0\ 10^{-15} m\ s^{-2}/\sqrt{Hz}$ for X and $4.0
\ 10^{-14} m\ s^{-2}/\sqrt{Hz}$ for Y and Z. For the angular degrees of
freedom, the values are of the order $3\ 10^{-12} rad\ s^{-2}/\sqrt{Hz}$ for
$\Theta_{SC}$ and $3\ 10^{-13} rad\ s^{-2}/\sqrt{Hz}$ for $H_{SC}$ and
$\Phi_{SC}$.
