The traditional small perturbation method is successfully used for linear dynamic analysis of gas bearings but excludes any nonlinear study. Investigating large displacements requires the evaluation of the nonlinear aerodynamic forces in the thin film. To avoid solving the unsteady compressible thin film fluid equations, we propose a method based on the use of frequency dependent dynamic coefficients and on the rational function approximation of the resulting impedances. Calculating impedances for several eccentricities enables mapping the full dynamic behavior of the bearing. A set of ordinary differential equations is then developed by using the inverse of Laplace transform. The equations of motion of the rotor are subsequently solved numerically with local linearization at each time step. The numerical results obtained by using impedances are in good agreement with the reaction forces obtained by solving the full nonlinear transient Reynolds equation.