The purpose of the study is to create and use a simple, but very effective mobile application available for use during the learning process, as well as for student's independent work after university hours. We have used the X code integrated development environment, developed by Apple for iPhone and iPad, in order to create the application. Our mobile application was used as an element of the digital educational resource in physics and mathematics. Natural and technical students have also used it to prepare for the interim assessment, external evaluation and a unified national testing. Using a mobile application allows a student to make up for the worn out or missing laboratory equipment, to use a large database of reference data without long searching, to create, modify and use software packages. The listed capabilities of a mobile application, ultimately, improve the quality of student's knowledge.

A mathematical model of turbulent motion of a non-homogeneous flow is constructed. Based on the pulsation energy balance method, a closed system of equations is obtained for calculating the average velocity and turbidity of a non-uniform flow. The calculation of the pulsation characteristics of the flow with a transverse shift is carried out and the analysis of the effect of the impurity on the pulsation structure of the turbulent flow and its effect on the motion of an unmanned aircraft is carried out. Since the safety assessment and service lifetime of an unmanned aerial vehicle cannot exclude the influence of disturbances in the atmosphere when calculating characteristics.

An unmanned aerial vehicle is a hardware and software complex with multi-purpose control. Unlike manned aviation, an unmanned aerial vehicle requires additional modules in its control system. These include the drone itself, the operator's workplace, software, data transmission lines and blocks necessary to fulfil the set flight objectives. The range of applications of unmanned aerial vehicles in the civil sector is not limited, but with the current state of the legal framework for the use of airspace, flight operations are somewhat difficult. The article formulates the main scientific position on the methodology of solving auxiliary tasks set in the work. The methodology specifies the main research stages, and it is a generalized methodological algorithm for the implementation of scientific research, which provides theoretical developments, field observations and simulation computer modelling. As a result of the study, it was found that the motion control systems of unmanned aerial vehicles are used for the process of their differentiation by the principle of complete external control, the advantages of which are considered in the work. For external control of divergence process of unmanned aerial vehicles, a method is considered for assessing the situation of convergence of unmanned aerial vehicles and choosing the manoeuvre of their difference using the area of dangerous courses, unmanned aerial vehicles approach, and it is possible to take into account the inertia of unmanned aerial vehicles when turning and the presence of navigational hazards that are in the manoeuvring area.

В работе рассматривается математическая модель движения, проводящей капли вязкой жидкости, погружающейся в диэлектрическую вязкую жидкость бесконечной протяженности и изменяющейся под влиянием капиллярности и электростатического отталкивания. Используя уравнения гидродинамики и электромагнетизма и ряд физически реалистичных предположений, мы сводим задачу к системе уравнений с частными производными. Решение такой системы уравнений является особенно сложным. Компьютерное моделирование в среде Сomsol Multiphysics позволило получить изменения формы заряженной капли со временем.

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