  In this paper we develop the new semi-analitical model of a tidally perturbed
or tidally disrupted star proposed recently by two of us. This model is
effectively a one dimensional Lagrangian model and it can be evolved
numerically much faster that the conventional 3D models. A self-consistent
derivation of the dynamical equations of the model is performed and several
important theorems about the dynamics of the model are proved without any
particular assumption about the equation of state of the stellar gas. The
dynamical equations are solved numerically for the case of $n=1.5$ polytropic
star evolving in the relativistic field of a $10^7M_{\odot}$ Kerr black hole.
Some results of these calculations are compared with the results of
calculations based on finite-difference 3D simulations. The comparison shows a
very good agreement between both approaches to the problem. Then we show that
the strength of the tidal encounter depends significantly on the relative
orientation of the orbital angular momentum of the star and the spin of the
black hole.
