  We present a variational model suitable for rapid preliminary design of atom
interferometers in a microgravity environment. The model approximates the
solution of the 3D rotating--frame Gross--Pitaevskii equation (GPE) as the sum
of Nc Gaussian clouds. Each Gaussian cloud is assumed to have time--dependent
center positions, widths, and linear and quadratic phase parameters. We applied
the Lagrangian Variational Method (LVM) with this trial wave function to derive
equations of motion for these parameters that can be adapted to any external
potential. We also present a 1D version of this variational model. As an
example we apply the model to a 1D atom interferometry scheme for measuring
Newton's gravitational constant, G, in a microgravity environment. We show how
the LVM model can (1) constrain the experimental parameter space size, (2) show
how the value of G can be obtained from the experimental conditions and
interference pattern characteristics, and (3) show how to improve the
sensitivity of the measurement and construct a preliminary error budget.
