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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.

Researchers meet the difficulties of experimental and computer modeling of a statics and dynamics of aircrafts connected with their essential nonlinearity. This is due to the fact that the aerodynamic effects of the interaction complex aircraft designs or their models with air environment generate abrupt changes of the character of the some dependencies. Aerodynamic coefficients in the model of interaction can be obtained only or by full-scale tests or by computer simulations. Therefore, the construction of mathematical models of the objects is associated with the mathematical processing of the points of the experimental data. In this case, the experimentally obtained dependence is usually essentially nonlinear up to piecewise, or even discontinuous nature. Approximation of such dependencies, even with the use of spline functions, is very difficult and is associated with large errors.

The paper formulated and solved the problem of investigating the traction and power characteristics of air-screw propulsor for airships. The study is performed by constructing a mathematical model relating the steady-state values of the shaft power and traction on the axis of the screw with the velocity of rotation and the actual velocity of the aircraft. Proved design scheme selection of computer simulation of aero-and thermodynamic processes occurring during rotation of the airscrew. Describes plan developed under the experimental task, providing variation in the basic parameters of the airscrew, motion parameters and flight environment The results of computer modeling of the interaction of the airflow with the airscrew at various combinations of these parameters. Results are shown in tabular and graphical form and as a mathematical model of the studied airscrew.

This paper is devoted to a method of creating of the automated ballonet system for pressure control inside an airship envelope. Along with the study of the effects of the positional control system parameters, the authors develop novel control scheme. It is based on a new hybrid controller, which combines positional approach to forming the output control signal with a contour of continuous correction of input signal, which defines the pressure drop on the surface of the envelope as a function of the flight altitude. This approach allows reducing the effect of self-oscillations of airship envelope internal pressure on the flight altitude. In order to prove the new approach the mathematical model is being obtained. The results of the derivation and simulations of the control system operation are presented in this paper.