  A new semi-analytical model of a star evolving in a tidal field is proposed.
The model is a generalization of the so-called 'affine' stellar model. In our
model the star is composed of elliptical shells with different parameters and
different orientations, depending on time and on the radial Lagrangian
coordinate of the shell. The evolution equations of this model are derived from
the virial relations under certain assumptions, and the integrals of motion are
identified. It is shown that the evolution equations can be deduced from a
variational principle. The evolution equations are solved numerically and
compared quantitatively with the results of 3D numerical computations of the
tidal interaction of a star with a supermassive black hole. The comparison
shows very good agreement between the main ``integral'' characteristics
describing the tidal interaction event in our model and in the 3D computations.
Our model is effectively a one-dimensional Lagrangian model from the point of
view of numerical computations, and therefore it can be evolved numerically
$10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model
well suited for intensive calculations covering the whole parameter space of
the problem.
