  Dynamical self-consistent constraints deduced from the Boltzmann equation are
necessary to analyse and interpret kinematic data in the Galaxy. It has been
shown that the standard epicycle theory approach, a first order theory to
estimate galactic characteristics, is subject to systematic errors. In some
recent work, distribution function solutions of the Boltzmann equation and/or
third moments in Jeans equations have been used to obtain a more consistent
description of our Galaxy. In this paper, we give a short review of
observational constraints and the different values usualy taken for global
parameters describing our Galaxy, namely the slope of the circular velocity
curve, the density and kinematic scale lengths. Secondly we build a new model
of Shu-type distribution functions where scale lengths and the shape of the
velocity curve are free parameters. Thirdly we compare and adjust this model to
velocity distributions of stars in the solar neighbourhood taken from the
Gliese catalogue and other ones. Implicit constraints are related to the
asymmetric drift relation and the Lindblad equation that gives the ratio of
radial and tangential velocity dispersions. We conclude that extended Shu
distribution functions recover most of the fundamental kinematic properties of
the galactic disc. We show that it is possible to build a consistent model
explaining local stellar kinematics and to determine local structural galactic
parameters.
