Rotor-Stator Rub is a rare but catastrophic phenomenon and in most cases leads to failure of Gas Turbine Engines. Asynchronous rub namely Partial Rub and Dry whip are two of the most common observed rub related phenomena. Dry whip leads to pure backward whirl and instability. This paper studies the dry whirl analytically to determine the boundaries of instability and establish expressions for nonlinear vibrations in case of dry whip. First, Nonlinear Natural Frequency has been defined for a rotor-stator rub system and expression for natural motion of the system has been formulated. Next, Pure rolling of rotor on stator has been used as a condition to approximate the nonlinear system to find out the dependence of dry whip frequency on the parameters such as stiffness, damping ratio, coefficient of friction and spin speed of the rotor. Moreover, a validation of the obtained frequencies and amplitudes obtained analytically has been performed through the simulation of rotor stator rub system using RK-4 integration technique. Furthermore, this study offers insight into the frequencies that are present in the Radial motion of the rotor and its source of origin. The radial displacement of the rotor has harmonics which are the result of interaction between the rotor speed and the backward whirl frequency causing dry whip.