Topic and aim. One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. This work aimed at creating the mathematical model of the non-contact atomic force microscope. Models and Methods.
One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. The lumped parameter model of the atomic force microscope in the non-contact operation mode is utilized to make the mathematical model of the micro cantilever of the AFM in this article.
The main moments of the historical development of one of the basic methods of nonlinear systems investigating (the averaging method) are traced. This method is understood as a transition from the so-called exact equation dx/dt = εX(t, x) (ε is small parameter), to the averaging equation dξ/dt = εX0(ξ) + ε2P2(ξ) + ... + εmPm(ξ) by corresponding variable substitution.Bogolyubov–Krylov’s approach to the problem of justifying the averaging method, based on the invariant measure theorem, is analyzed.
