In this paper we investigated the analytical properties of the dispersion relations of the equation of internal gravity waves with model and arbitrary distributions of the buoyancy frequency. For the analytical solution of the problem we used the model distribution of the buoyancy frequency, which is used in applied oceanological calculations in the presence of a seasonal thermocline. We have obtained implicit forms of dispersion dependences, which are expressed in terms of the Bessel function of the real index. For wave numbers other than zero, we proposed an asymptotic method for studying the dispersion relation, based on the construction of Bessel functions uniform asymptotics for large values of the real index and argument, which are expressed in terms of the Airy functions. For an arbitrary distribution of the buoyancy frequency, using the perturbation method and the WKBJ method, we obtained asymptotic representations of the dispersion relations for small wave numbers. The solutions constructed in this work make it possible to further calculate the amplitude-phase characteristics of the fields of internal gravity waves with model and arbitrary buoyancy frequency distributions

Calibration of the inertial sensors and the entire inertial measurement units (IMUs), as a rule, is carried out using special equipment such as turn-tables. However, for micromechanical (MEMS) modules, the use of such high-precision equipment is not reasonable due to high noise and varying parameters of measurement model for a particular device. Existing algorithmic solutions for calibrating MEMS IMUs either use an oversimplified IMU measurement model or require quite a lot of time to solve the problem. Therefore, this paper considers the application of a dual Kalman filter to the measurement model parameters estimation of a three-axis MEMS angular velocity sensor. The measurement model under consideration includes scale factors and sensor zero offsets. To solve the problem, several modifications are made to the classical dual Kalman filter. To confirm the applicability of the proposed algorithm, computational experiment was carried out, in which the IMU measurements are modeled according to the true known measurement model. The results of computational experiment have shown the applicability of the proposed approach and a sufficiently high accuracy of obtained estimates

This article discusses an algorithm that allows you to calculate the GPS coordinates of an object detected in images taken from an unmanned aerial vehicle (quadcopter). The developed algorithm can be used in the tasks of detecting various objects and then plotting their coordinates on maps. The authors of the article describe an approach to solving this problem, identify the main stages of the algorithm. An approach to writing a program implemented in the C++ programming language using the OpenCV open source library (machine vision library) is described. The results of the program are demonstrated. The authors managed to achieve the accuracy of calculating the GPS coordinates of objects of the order of one meter, which is comparable to the accuracy of satellite positioning of a quadcopter from which aerial photography of the underlying surface is carried out.

The paper investigates the influence of the configuration of the control surfaces of a space launch vehicle (SLV), in the most critical section of the flight phase of the first stage, on the efficiency of the guidance system. As the control surfaces are considered the main vectored engines with variable thrust vector. At present considerable efforts have been made in the Russian Federation to develop reusable space launch vehicles, which will reduce production costs, as well as the reuse of the first stage will reduce the landing operations area, which will have a positive effect on the ecology of the surrounding area. When developing a perspective reusable space launch vehicle, an analysis of the influence of the number of engines and the variant of their configurations on the stability and controllability will allow predicting the advisability of choosing the layout of these engines, at the stage of preliminary design. The analysis was effected in the pitch and yaw channels, using the perturbation equation of motion of the SLV. The conducted computation of the dependence of the controlled and disturbing moment on the flight time, as well as the loading of the control elements allowed to exclude unacceptable layouts and to choose the most perspective and effective variants of the location of the SLV main engines. In the early stages of development of reusable SLV, this result will be a necessary tool for solving problems of controllability at the predesign stage, and evaluation of the degree of unification of the 1st and 2nd stage recovery block main engines.

In this paper, in the case of two independent spatial variables, a system of equations of motion of a continuous medium with constant values of density and temperature is considered. Solutions of the Cauchy problem for this nonlinear system of partial differential equations are presented in the form of trigonometric series. An infinite system of ordinary differential equations is constructed to find the coefficients of time-dependent trigonometric series. The convergence of the trigonometric series used is proved. The theorem on multiple frequencies is also proved, describing the appearance of harmonics in the solution, which did not exist in the initial conditions.

The solution of load balancing problem in parallel programming is very actual problem. One of the original methods for solving the balancing problem is the use of Voronoi diagrams. The main advantage of the following method that it can be used on the data of different types. For example, this method can be used for balancing the Eulerian and Lagrangian computational grids with the smooth-particles hydrodynamic method. Also, this approach can be used for adaptive grids. However, in that case, due to the strong inhomogeneity of the load on adaptive grids, the such load balancing method can be unstable or have poor convergence. In the present work we give an improvement of the load balancing method in terms of weighted Voronoi diagrams. The proposed algorithm is implemented as a software package. Testing of the proposed algorithm is based on a number of model problems and problems from the field of continuum mechanics. Evaluation of the balancing efficiency is based on the study of the behavior of the imbalance value with and without balancing. It is shown that the proposed algorithm successfully copes with its task and the magnitude of the imbalance in the case of using a weighted Voronoi diagram is 10–100 times less than when using classical Voronoi diagrams.