  LISA-Pathfinder is an ESA space mission flown between 2015 and 2017 to
demonstrate a technological maturity sufficient for building a gravitational
waves telescope in space, such as the Laser Interferometer Space Antenna
(LISA). A pair of cubic test masses is hosted inside the LISA-Pathfinder
spacecraft and shielded from any force other than the interplanetary
gravitational field. The purity of the shielding gives the performance of the
mission.
  There are a number of aspects that had to be confirmed in-flight. One of them
is the transition phase from the launch configuration, when the test masses are
locked, to the science free-falling configuration. Each test mass is initially
released from the mechanical constraints via a dedicated mechanism and then
captured by an electrostatic control system. In fact, each test mass is
surrounded by a set of electrodes for actuation and sensing purposes. The
performance criterion of the release is the final velocity of the test mass
relative to the spacecraft, with an upper threshold set to 5 $\mu m/s$. The
LISA-Pathfinder first in-flight release velocities highlighted an unexpected
dynamics with large linear and angular velocities. The electrostatic control
was successful, but only relying on a manual procedure that cannot be
considered as baseline for LISA.
  This paper helps investigating the in-flight non-compliance by dealing with
the modeling of the electrostatic environment around each test mass and its
contribution to the release and capture dynamics. The electrostatic model is
based on the method of moments, a boundary element numerical technique suitable
for estimating forces and capacitances between conductors. We also provide a
short overview of the method, which can be used for the analysis of other
phenomena within LISA and for the design of future gravitational waves
telescopes and space projects.
