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Mathematical modeling of technical objects is most frequently connected with mathematical processing of experimental data. The obtained pointlike dependencies of output variables on input ones are often strongly nonlinear, piecewise, and sometimes discontinuous. Approximation of these dependencies using polynomial resolution and spline-functions is problematic and may cause low accuracy. A radically new solution to this problem was suggested in a number of previous works. The method is based on partitioning of experimental dependencies into patches, approximation of each patch by analytic functions, multiplicative cutting of fragments from each function along the patch border and additive gluing of the fragments into a single function -- namely the model of approximated dependence. The analytic properties of this approximating glued function appear to be the major distinguishing feature and advantage of the method.

The main difficulties of the mathematical models vehicles creation are defined by strongly nonlinearity of dependences which connect various variables their states and conditions of the movement environment. Most it belongs to aircrafts as aerodynamic interactions are characterized by essential nonlinearity up to discontinuity of variables and their derivatives. Creation process of these models is complicated by high-dimensionality, characteristic for the mechanical movement laws. Experimental creation of the mathematical models (MM) of such dependences is carried out by various mathematical methods of approximation of data. Universal remedies of the solution of the formulated task don't exist. Each of it possesses both benefits, and considerable shortcomings. In this regard the possibilities of a method creation of high-precision analytical approximations of the strongly nonlinear dependences using the analytical functions have been investigated.