In terms of stationary open water flow, the boundary conditions in the flow free spreading problem are reduced to a dimensionless form by the various coordinates and flow parameters’ transformations, including I.A. Sherenkov’s transformations, which bring the boundary value problem to a dimensionless form. It was found that the equations system itself can be reduced to a universal dimensionless form, but the boundary problem cannot be reduced, since the boundary conditions both at the flow outlet from a free-flow pipe and at the flow infinity downstream are not reduced to a universal dimensionless form. It is concluded that it is impossible to solve the boundary value problem once and then use this solution under any boundary conditions. It was also revealed that the problem solution depends on a dimensionless parameter-the Froude criterion at the flow outlet from the pipe. This proves that it is possible to build a universal graph, a universal method for solving the problem with Froude numbers at the flow outlet from the pipe more than unity or close to unity. But increasing the Froude number, it is necessary to build a series of graphs, and it is better to create a single theory, an algorithm for solving this problem.

In the market economy major active players (or agents, or subjects), i.e. buyers and sellers of goods and commodities, behave to a certain extent in a deterministic way thus subordinating their behavior in the market to some strict economic laws. The fact that these laws are of a descriptive nature, and they have not yet been expressed in a precise mathematic language, is not of key importance in this case.Every rational player or market subject acts in the market in accordance with a strict rule of obtaining maximum profit or benefit or some other criterion of optimality for him or her and in this respect market economic systems resemble physical systems where all players, members, and elements of the system act also in accordance with some principles of maximization.The main drive of our research is that we assume general possibility to develop dynamic models for relatively simple market economic systems consisting of an economic subsystem or simply an economy with a certain number of buyers and sellers and its external environment with certain interactions between economy agents, and between the economy and environment. In this case, it is supposed that it can be performed by the analogy with the method of developing theoretical models of physical systems consisting of a system of interacting material particles in the external fields or external environment [1, 2]. Moreover, it is assumed that equations of motion derived for physical systems in the physical space are quite a good initial approximation for equations of motion of modeled economic systems in some price space.Let's give the following reasons to substantiate such an approach. Let p(t) be a trajectory of movement of the market subject in a price space, in other words, it is price p of a commodity set for by the subject at a moment t. By setting prices this way, buyers and sellers who act as homo negotians (a negotiating man) in a physical modeling aim at maximum satisfaction of their strive for profit, i.e. for such price at which interests of both buyers and sellers and, considering external environment and the whole system in general, are satisfied in an optimal way. It is here that one can see similarity of the movement of economy (described by

The paper presents the hydropneumatic suspension mathematical and simulation model development results for the grain combine harvester adapter. The urgency of the work in connection with the hydropneumatic suspensions spread and the need to increase the system efficiency for field relief copying has been substantiated. A computational model of a hydropneumatic suspension including hydraulic cylinders and hydropneumatic shock absorbers connected in parallel to them, including chokes and gas springs has been presented. A system of equations for the hydraulic cylinder piston motion, depending on the hydropneumatic suspension parameters and the number of the connected hydropneumatic shock absorbers has been presented. On the assumption basis, a simplified diagram of the adapter hydropneumatic suspension with back pressure and the corresponding equation system for determining the hydraulic cylinder piston movement have been drawn up. The model includes changing the parameters of external influence on the system, as well as the hydropneumatic accumulator presetting parameters. To assess the developed model’s performance, its simulation model, which was integrated into the well-known simulation model of the grain combine harvester movement, has been compiled. The modeling results of the combine movement on the field with real geometric evenness parameters have been presented. Based on the simulation results, an oscillogram of the hydraulic cylinder piston movement has been shown, depending on the hydropneumatic accumulators’ settings. Conclusions and directions for further research in this area have been presented.

The basic system of equations of motion of a non-stationary two-dimensional open water flow is obtained, which does not contradict the previously known system for a stationary flow.

The paper studies a two-dimensional water flow from a non-pressure rectangular or round pipe placed into a wide horizontal channel. To simplify the problem, the real three-dimensional flow is modeled as a two-dimensional zone by eliminating the liquid particles’ velocities and accelerations in the direction perpendicular to the flow zone. To describe the water flow motion law, L. Euler’s equations for the ideal fluid are used, taking into account the continuity equations and the Bernoulli equation. The two-dimensional flow models in the spreading zone with the adequacy degree sufficient for practice, describe the movement of water flows arising in the lower road drainage systems races, Liman irrigation systems, small bridges, water volley channels, various culverts and water-crossing facilities. The obtained dependences of the velocity distribution, depth and water flow geometry give an accuracy exceeding that known by the previously used methods both by the velocity values and by the boundary current lines geometry.