We present a fully consistent evolutionary disc model of the solar cylinder .
The model is based on a sequence of stellar sub-populations described by the star formation history ( SFR ) and the dynamical heating law ( given by the age-velocity dispersion relation AVR ) .
The stellar sub-populations are in dynamical equilibrium and the gravitational potential is calculated self-consistently including the influence of the dark matter halo and the gas component .
The combination of kinematic data from Hipparcos and the finite lifetimes of main sequence ( MS ) stars enables us to determine the detailed vertical disc structure independent of individual stellar ages and only weakly dependent on the IMF .
The disc parameters are determined by applying a sophisticated best fit algorithm to the MS star velocity distribution functions in magnitude bins .
We find that the AVR is well constrained by the local kinematics , whereas for the SFR the allowed range is larger .
The model is consistent with the local kinematics of main sequence stars and fulfils the known constraints on scale heights , surface densities and mass ratios .
A simple chemical enrichment model is included in order to fit the local metallicity distribution of G dwarfs .
In our favoured model A the power law index of the AVR is 0.375 with a minimum and maximum velocity dispersion of 5.1 km/s and 25.0 km/s , respectively .
The SFR shows a maximum 10 Gyr ago and declines by a factor of four to the present day value of 1.5 M _ { \mathrm { \sun } } / \mathrm { pc } ^ { 2 } / \mathrm { Gyr } .
A best fit of the IMF leads to power-law indices of -1.46 below and -4.16 above 1.72 M _ { \mathrm { \sun } } avoiding a kink at 1 M _ { \mathrm { \sun } } .
An isothermal thick disc component with local density of \sim 6 \% of the stellar density is included .
A thick disc containing more than 10 % of local stellar mass is inconsistent with the local kinematics of K and M dwarfs .
Neglecting the thick disc component results in slight variations of the thin disc properties , but has a negligible influence on the AVR and the normalised SFR .
The model allows detailed predictions of the density , age , metallicity and velocity distribution functions of MS stars as a function of height above the mid-plane .
The complexity of the model does not allow to rule out other star formation scenarios using the local data alone .
The incorporation of multi-band star count and kinematic data of larger samples in the near future will improve the determination of the disc structure and evolution significantly .