The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for obtaining a precise response. Furthermore using the presented closed form solutions for the squeezed film damping torque, it is proved that when the tilting angle of the mirror is small, the damping is linear viscous one, while when the tilting angle is finite, the damping would be linearly proportional with the angular velocity of the mirror and at the same time it is a nonlinear function of the tilting angle of the mirror. Results of this paper can be used for accurate dynamical simulation of micromirrors with presence of the squeezed film damping.

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