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The paper presents studies of the system "induction generator-induction motor" with parametric asymmetry on a mathematical model to determine the quality of generated electricity in load operating modes. A mathematical model of the "induction generator-induction motor" system has been developed taking into account losses in steel and parametric asymmetry. The analysis of the transient characteristics of an induction generator when a motor load is connected in symmetrical and asymmetrical modes of operation is carried out. The results of changes in the main characteristics of an induction motor at various degrees of parametric asymmetry in the generator are presented. The quality of the generated electricity was analyzed based on the calculations of the unbalance coefficients for each of the operating modes. The assessment of the thermal state in steady-state conditions was carried out using an equivalent thermal equivalent circuit. Thermal transients were investigated when starting an induction motor from an autonomous energy source based on an induction generator. On a thermal mathematical model, the study of the effect of the output voltage asymmetry on the heating of the connected induction motor was carried out. It is shown that the asymmetry of the output voltage of an induction generator reaches 3–10 % and causes overheating of the windings in excess of the permissible values. A regression model has been developed for studying the operating conditions of an induction motor when powered by an induction generator with an asymmetry of the stator windings. The use of the obtained equations will make it possible to determine the most rational combination of factors affecting the heating of the stator windings of induction machines, in which they will not overheat above the maximum permissible temperature values of the corresponding insulation classes, Представлены исследования системы «асинхронный генератор-асинхронный двигатель» с параметрической несимметрией на математической модели для определения качества генерируемой электроэнергии в нагрузочных режимах работы. Разработана математическая модель системы «асинхронный генератор-асинхронный двигатель» с учетом потерь в стали и параметрической несимметрией. Выполнен анализ переходных характеристик асинхронного генератора при подключении двигательной нагрузки при симметричных и несимметричных режимах работы. Представлены результаты изменения основных характеристик асинхронного двигателя при различной степени параметрической несимметрии в генераторе. Качество генерируемой электроэнергии анализировалось на основе расчетов коэффициентов несимметрии для каждого из режимов работы. Оценка теплового состояния в установившихся режимах выполнена с использованием эквивалентной тепловой схемы замещения. Исследованы тепловые переходные процессы при пуске асинхронного двигателя от автономного источника энергии на базе асинхронного генератора. На тепловой математической модели проведено исследование влияния несимметрии выходного напряжения на нагрев подключаемого асинхронного двигателя. Показано, что несимметрия выходного напряжения асинхронного генератора достигает 3–10% и вызывает перегрев обмоток сверх допустимых величин. Разработана регрессионная модель для исследований условий работы асинхронного двигателя при питании от асинхронного генератора с несимметрией обмоток статора. Использование полученных уравнений позволит определять наиболее рациональное сочетание факторов, влияющих на нагрев статорных обмоток асинхронных машин, при которых они не будут перегреваться сверх предельно допустимых значений температуры соответствующих классов изоляции, Представлені дослідження системи «асинхронний генератор-асинхронний двигун» з параметричною несиметрією на математичній моделі для визначення якості генерованої електроенергії в навантажувальних режимах роботи. Розроблено математичну модель системи «асинхронний генератор-асинхронний двигун» з урахуванням втрат в сталі і параметричної несиметрії. Виконано аналіз перехідних характеристик асинхронного генератора при підключенні двигунного навантаження при симетричних і несиметричних режимах роботи. Представлені результати зміни основних характеристик асинхронного двигуна при різному ступені параметричної несиметрії в генераторі. Якість генерованої електроенергії аналізувалася на основі розрахунків коефіцієнтів несиметрії для кожного з режимів роботи. Оцінка теплового стану в сталих режимах виконана з використанням еквівалентної теплової схеми заміщення. Досліджено теплові перехідні процеси при пуску асинхронного двигуна від автономного джерела енергії на базі асинхронного генератора. На тепловій математичній моделі проведено дослідження впливу несиметрії вихідної напруги на нагрів підключеного асинхронного двигуна. Показано, що несиметрія вихідної напруги асинхронного генератора досягає 3–10% і викликає перегрів обмоток понад допустимих величин. Розроблено регресійну модель для досліджень умов роботи асинхронного двигуна при живленні від асинхронного генератора з несиметрією обмоток статора. Використання отриманих рівнянь дозволить визначати найбільш раціональне поєднання чинників, що впливають на нагрів статорних обмоток асинхронних машин, при яких вони не будуть перегріватися більше гранично допустимих значень температури відповідних класів ізоляції

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Using wireless synchronization in GPR studies, we observe the stepwise effects on the hodograph images, resulting from a great increase in the distance between the receiving and transmitting antenna units. As the transmitter-receiver offset increases, reflections from the upper layers can be completely lost, resulting in the overestimation of velocities in the layered structures.

This study can be useful especially in education purposes because the authors, based on the theoretical analysis, verify the obtained results using two programming environments, Labview and Matlab, for the study of the systems stability beginning with the transfer function. There are shown two cases, for stable system and unstable system. It is highlighted the pole location and zeros, the Nyquist hodograph, the geometrical interpretation of the roots and Bode diagram. The corectitude of the theoretical analysis and the virtual methods that are used, lead to obtaining identical results.

We conducted a study of the inertial oscillations of the speed of currents in Peter the Great Bay, induced by typhoon Lionrock. The study is based on the measurements of the moored acoustic Doppler current profiler. Data analysis showed that under the action of the typhoon a field of currents with inertial oscillations (IO) of anomalous characteristics was formed in the bay. It is found that the spectral energy of the IO of currents with left and right rotation are of the same order while the major axis of the hodograph of the speed of these currents exceeds its small axis by an order of magnitude. A change of the inertial frequencies of the currents with cyclonic rotation, as well as the “red shift” of this frequency in the bottom and the “blue shift” in the surface layer of the inertial currents with anticyclonic rotation were found. Parametric IO interaction with anticyclonic rotation and the synoptic component of the currents with the same direction of rotation was detected. It has been suggested that the anomalous characteristics of inertial currents with two types of rotation are due to their interaction with the low-frequency component of the stream of Primorsky Current induced by the typhoon.

A fully-saturated lens of steady fresh groundwater floating in a homogeneous and isotropic desert sandy aquifer is analytically studied based on a hydrological model by Kunin and interface solution by Van Der Veer. A static saline groundwater is beneath the lens. A phreatic surface of moving fresh water inside the lens is partially recharged (either naturally or by managed aquifer recharge) from the vadose zone and partially exfiltrates to it. A spatially focused recharge and intensive evapotranspiration preserve a steady downward-upward topology of fresh water motion. In terms of the 1-D Dupuit-Forchheimer approximation in a horizontal in-lens saturated flow a boundary value problem (BVP) for an ODE for the Strack potential is solved. The shape of the water table and, based on the Ghijben-Herzberg assumption, the interface are found. The total volume of the positive-pore pressure water flowing within the lens is evaluated. Constant infiltration and evaporation rates as well as evaporation linearly decreasing with depth of the water table (counted from the ground surface) are considered. The case of 2-D flow is tackled by the Toth model. A triangular analytic element approximates a half of the flow domain and consists of an isobaric side and two no-flow sides. Conformal mapping of this triangle onto a reference plane and solution of the Dirichlet BVP in a half-plane deliver the distribution of infiltration-exfiltration intensity along the water table, total flow rate and locus of the hinge point. A mathematically more cumbersome approximation of the flow domain assumes the water table to be a tilted straight line but the interface to be found as a free boundary. Solution of the corresponding BVP uses a curvilinear triangle in the hodograph plane.

We consider theoretical foundations for the nondestructive testing of large-sized structures and structures made of structurally inhomogeneous composite materials by the method of elastic-wave velocity hodograph. The theoretical fundamentals of the method of elastic-wave velocity hodograph are presented for a single-layer medium, and the propagation of low-frequency elastic waves in a homogeneous isotropic single-layer medium is described. Based on the research, recommendations are given on detecting defects and determining the speed of propagation of elastic waves in a single-layer medium; this allows nondestructive testing of the physical and mechanical characteristics of the material in the layer and flaw detection and thickness gaging in large-sized structures and structures made of coarse-grained and composite materials.

Classical techniques for initial orbit determination (IOD) require the analyst to find a body’s orbit given only observations such as bearings, range, and/or position. In these cases, one of the goals is often to solve for the unknown velocity vector at one or more of the observation times to fully define the orbit. Recently, however, a new class of IOD problems has been proposed that switches the knowns and unknowns in these classic IOD problems. Specifically, the objective is to find the unknown position vectors given only velocity measurements. This paper presents a detailed assessment of the geometric properties of this new family of velocity-only IOD problems. The primary tool for this geometric analysis is Hamilton’s orbital hodograph, which is known to be a perfect circle for all orbits obeying Keplerian dynamics. This framework is used to produce intuitive and efficient algorithms for IOD from three velocity vectors (similar structure to Gibbs problem) and for IOD from two velocity vectors and time-of-flight (similar structure to Lambert’s problem). Performance of these algorithms is demonstrated through numerical results.

Two-dimensional plastic flow of a flange when deep drawing a thin-walled polygonal prism with a flat bottom of round blank provided with Mises yield criterion based on the theory of plane stress condition according to Sokolovskii is simulated. The slip lines, the stress condition, the hodograph of displacement velocities, and the dissipative function of plastic flow are calculated. The limit parameters of deep drawing are defined by the maximum tensile stress at the mold contour and by zones with negative dissipative function, which depends on the radius of rounding of mold angles and the prism height.

The coupled task allocation and path planning problem for heterogeneous multiple unmanned aerial vehicles performing a search and attack mission involving obstacles and no-fly zones are addressed. The importance of the target is measured using a time-dependent value. A task allocation algorithm is proposed to obtain the maximum system utility. In the system utility function, the reward of the target, path lengths of unmanned aerial vehicles, and number of unmanned aerial vehicles to perform a simultaneous attack are considered. The path length of the unmanned aerial vehicles based on the Pythagorean hodograph curve is calculated, and it serves as the input for the task allocation problem. A resource management method for unmanned aerial vehicles is used, so that the resource consumption of the unmanned aerial vehicles can be balanced. To satisfy the requirement of simultaneous attacks and the unmanned aerial vehicle kinematic constraints in an environment involving obstacles and no-fly zones, a distributed cooperative particle swarm optimization algorithm is developed to generate flyable and safe Pythagorean hodograph curve trajectories for unmanned aerial vehicles to achieve simultaneous arrival. Monte Carlo simulations are conducted to demonstrate the performance of the proposed task allocation and path planning method.

The paper presents hodograph transformations between nonlocal short pulse models and the first member in the Ablowitz–Kaup–Newell–Segur negative hierarchy (AKNS( − 1 )). Multi-component cases are also considered. It is shown that the independent variables of the short pulse models and AKNS( − 1 ) that are connected via hodograph transformations are covariant in nonlocal reductions.

A self-similar flow generated by water entry of an expanding two-dimensional smooth and curved body is studied based on the incompressible velocity potential theory, with gravity and surface tension effects being ignored. At each expansion speed, mathematical solutions for detached flow with a splash jet and attached flow with jet leaning on the body surface are obtained, both of which have been found possible in experiment, corresponding to hydrophobic and hydrophilic bodies, respectively. The problem is solved using the integral hodograph method, which converts the governing Laplace equations into two integral equations along the half real and imaginary axes of a parameter plane. For the detached flow, the conditions for continuity and finite spatial derivative of the velocity at the point of flow departing form the body surface are imposed. It is found that the Brillouin–Villat criterion for flow detachment of steady flow is also met in this self-similar flow, which requires the curvatures of the free surface and the body surface to be the same at the detachment point. Solutions for the detached flow have been obtained in the whole range of the expansion speeds, from zero to infinity, relative to the water entry speed. For the attached flow there is a minimal expansion speed below which no solution cannot be obtained. Detailed results in terms of pressure distribution, free surface shape and streamlines and tip angle of the jet are presented. It is revealed that when solutions for both detached and attached flows exist, the pressure distributions on the cylinder surface are almost the same up to the point near the jet root. Beyond that point, the pressure relative to the ambient one drops to zero at the detachment point in the former, while it drops below zero in the jet attached on the body and then returns to zero at the contact point in the latter.

This paper is focused on the existence of classical sonic-supersonic solutions near sonic curves for the two-dimensional pseudo-steady full Euler equations in gas dynamics. By introducing a novel set of change variables and using the idea of characteristic decomposition, the Euler system is transformed into a new system which displays a transparent singularity-regularity structure. With a choice of weighted metric space, we establish the local existence of smooth solutions for the new system by the fixed-point method. Finally, we obtain a local classical solution for the pseudo-steady full Euler equations by converting the solution from the partial hodograph variables to the original variables.

This paper focuses on a degenerate boundary value problem arising from the study of the two-dimensional Riemann problem to the nonlinear wave system. In order to deal with the parabolic degeneracy, we introduce a partial hodograph transformation to transform the nonlinear wave system into a new system, which displays a clear regularity–singularity structure. The local existence of classical solutions for the new system is established in a weighted metric space. Returning the solution to the original variables, we obtain the existence of classical solutions to the degenerate boundary value problem for the nonlinear wave system.

A new method to design a cubic Pythagorean-hodograph (PH) spline curve from any given control polygon is proposed. The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has $$G^1$$ continuity or curvature continuity. The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines, for example, the convex hull and variation-diminishing properties.

An analytical solution of the impulsive impact of a cylindrical body submerged below a calm water surface is obtained by solving a free boundary problem. The shape of the cross section of the body is arbitrary. The integral hodograph method is applied to derive the complex velocity potential defined in a parameter plane. The boundary-value problem is reduced to a Fredholm integral equation of the first kind in the velocity magnitude on the free surface. The velocity field, the impulsive pressure on the body surface, and the added mass are determined in a wide range of depths of submergence for various cross-sectional shapes, such as a flat plate, a circular cylinder, and a rectangle.

How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. We diagnose profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. We propose an analytic relationship between energy spectra and divergence amplitudes, which, if confirmed by future studies, could be used to design better external forcing methods for regional models.

We implement and verify for the first time four Weather Research and Forecasting (WRF) model urban configurations, focused on the coastal metropolitan area of Tel-Aviv (MTA) using updated land use and urban morphological maps. We analyze the mesoscale summertime flow and the urban canopy (UC) role in the occurrence of different hodograph dynamics observed within MTA at night. These events may be significant in the context of air quality research. The four configurations – bulk (MM), single-layer (SLUCM), multi-layer (BEP), and BEP coupled with the building energy model (BEPBEM) – reproduce the observed diurnal temperature and wind diurnal cycles, with similar 10m wind direction bias and RMSE (15° and ~30°, respectively), with preference for MM and SLUCM at night. However, the SLUCM shows the lowest skill for the 10m wind speed (WS) (bias and RMSE equal or larger than 1ms-1), and the BEP shows the largest underestimation of the 2m temperature, ~-2.5°C. In the SLUCM, the WS increases over an UC region and with increasing building heights. The simulations show that at night, a convergence line (CL) builds up with the urban heat island, downstream of the NW flow. West of the CL, the wind continues flowing from the sea, and rotates anti-clockwise to form a non-elliptical sea-breeze hodograph. Removing MTA UC restores an elliptical hodograph. East of the CL, the UC supports an elliptical hodograph with a clockwise rotation through the NE sector, previously reported as dynamically unstable. We expect such wind hodograph dynamics within similar coastal metropolitan areas.

The Navier-Stokes equations presented in a previous chapter assumed no horizontal mean shear. However, coastal modelers should use a specialized, sophisticated form of these equations that take into account horizontal shear. Moreover, improved representations of friction are also included here, in the more complete Navier-Stokes equations. These improvements are indeed important in the coastal zone, where great differences in the vertical shearing stress occur across space. These revised equations are sometimes referred to as the Reynolds stress forms of the equations of motion, because they include explicit representation of the shearing stress. In addition, an imaginary component is introduced into the Navier-Stokes equations under hydrostatic conditions, for representing flow in the Ekman spiral. This allows for the simultaneous solution of both the downwind and crosswind components of wind velocity (u and v, respectively) and as a function of the other variables in the problem. This is necessary because u and v have an intrinsic relationship with each other due to the angle of the wind. The complete derivation of this classical Ekman spiral is then shown in step-by-step fashion. The chapter concludes with some real-world application of this solution, in the form of a hodograph and in showing how wind direction changes with height can affect coastal weather.

The two-dimensional nonlinear problem of steady flow past a body submerged beneath an elastic sheet is considered. The mathematical model is based on the velocity potential theory with fully nonlinear boundary conditions on the fluid boundary and on the elastic sheet, which are coupled throughout the numerical procedure. The integral hodograph method is employed to derive the complex velocity potential of the flow which contains the velocity magnitude on the interface in explicit form. The coupled problem has been reduced to a system of nonlinear equations with respect to the unknown magnitude of the velocity on the interface, which is solved using a collocation method. Case studies are undertaken for both subcritical and supercritical flow regimes. Results for interface shape, bending moment and pressure distribution are presented for the wide ranges of Froude numbers and depths of submergence. According to the dispersion equation, two waves on the interface may exist. The first, longest wave is that caused by gravity, and the second, shorter wave is that caused by the elastic sheet. The obtained solution exhibits strongly nonlinear interaction of these waves above the submerged body. It is found that near the critical Froude number, there is a range of submergences in which the solution does not converge.

We solve the problem of G2∕C1 Hermite interpolation (i.e. interpolation of prescribed boundary points as well as first derivatives and curvatures at these points) by planar quintic Pythagorean Hodograph B-spline curves with one free interior knot which acts as a shape parameter. We present conditions on the data ensuring the existence of solutions. Finally, we illustrate the influence of the interior knot on the shape of the resulting interpolant and on the values of the absolute rotation index or the bending energy.

A method for constructing a solution for some systems of first-order quasilinear partial differential equations is presented. The type of equations can either be hyperbolic or elliptic. The method is based on the application of the generalized hodograph method, which allows us to write the solution in an implicit form. There is a system of first-order linear partial differential equations that is used for commuting flows in the generalized hodograph method. We discover an analogy between the commuting flows and divided differences for the Hermite polynomial. This analogy allows us to obtain an explicit representation for commuting flows. The introduction of new (Lagrangian) variables, which are conserved on the characteristics of the original system, suggests a way to transform the solution of the Cauchy problem for first-order quasilinear partial differential equations to the solution of the Cauchy problem for ordinary differential equations. Numerical, and in some cases analytical, integration of the Cauchy problem makes it possible to construct explicit solutions of the problem on the level lines (isochrons) of the implicit solution. The method proposed is significantly different from the grid method, finite element method, finite volume method, and, in fact, is more precise. The error of the solution can arise only at the last stage in the numerical integration of the Cauchy problem for ordinary differential equations. Moreover, the method allows us to obtain multivalued solutions, in particular, to study the process of wave breaking in hyperbolic systems. Particular cases of the equations considered here describe diffusion-free approximation in a wide range of mass transport processes in multicomponent mixtures, such as electrophoresis, chromatography, centrifugation. As a simple example, the solution of the electrophoresis problem (separation multicomponent mixture to individual component) is presented.

Using the model of fast phase transitions and previously reported equation of the Gibbs-Thomson-type, we develop an equation for the anisotropic interface motion of the Herring-Gibbs-Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship 'velocity - Gibbs free energy', Klein-Gordon and Born-Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'. © 2021 The Authors. Data accessibility. Electronic supplementary material on asymptotic analysis of the hyperbolic phase field model are attached to the main text of the manuscript. Authors’ contributions. Both authors contributed to the derivation, analytical treatments and analysis of results. A.S. carried out calculations for comparison of the analytical equation with data of molecular dynamics simulations. Competing interests. We declare we have no competing interests. Funding. The funding has been made for P.K.G. by German Science Foundation (DFG-Deutsche Forschungsgemeinschaft) under the Project GA 1142/11-1. Acknowledgements. Authors thank Jeffrey J. Hoyt for his valuable explanations about molecular dynamic simulation data of Ni. P.K.G. acknowledges financial support of German Science Foundation (DFG-Deutsche Forschungsgemeinschaft). A.S. thanks M. Bennai for hosting the present work in the research activities of LPMC.

This paper extends previous results of the same authors on the determination of the polynomial root distribution with respect to a sector by means of elementary vector analysis. Specifically, it is shown how the overall phase variation of any real or complex polynomial along the radii of a sector accounts for the number of roots inside and outside the sector. The method applies to both symmetric and asymmetric sectors with respect to the real axis. Its practical application only requires plotting a Nyquist-like diagram (a hodograph). The procedure proves particularly useful in the stability analysis of fractional-order systems. A pair of examples is worked out to show how the method operates.

Радиозондовые данные измерений скорости ветра, выполненные 28 февраля и 15 ноября 2007 года, были использованы для идентификации внутренних гравитационных волн (ВГВ) и определения их характеристик в нижней стратосфере Земли над Кокосовыми островами (координаты:12.04°S; 96.90°E). Анализ годографа скорости ветра показал, что наблюдаемые флуктуации индуцированы волнами, энергия которых распространяется вверх. Используя результаты анализа годографа скорости ветра, дисперсионное уравнение и поляризационные соотношения, мы определили величины ключевых характеристик ВГВ, таких как собственная частота, амплитуды вертикальных и горизонтальных возмущений скорости ветра, собственная вертикальная и горизонтальная фазовые (и групповые) скорости, кинетическая и потенциальная энергия волн. Предложен оригинальный метод определения волновой частоты в системе отсчета земного наблюдателя и азимутального направления распространения ВГВ в атмосфере. Приложение разработанного метода к радиозондовым измерениям, выполненным 28 февраля 2007 года, дало возможность установить, что волновая частота в системе земного наблюдателя равна 14.0·10–4 рад/с и она соответствует периоду волны T=1.25 часа., Radiosonde measurement data of the wind speed, conducted 28 February and 15 November2007, have been used for the internal gravity waves (IGWs) identification and determination of their parameters in the Earth’s lower stratosphere over Cocos Islands (coordinates:12.04°S;96.90°E). A wind speed hodograph analysis has shown that observed fluctuations are wave-induced while the wave energy propagates upwards. Using the results of wind speed hodograph analysis, dispersion equation and polarization relationships, we have obtained the magnitudes of key IGWcharacteristics such as the intrinsic frequency, amplitudes of vertical and horizontal perturbations of the wind velocity, vertical and horizontal wavelengths, intrinsic vertical and horizontal phase (and group) speeds, wave kinetic and potential energy. An original method for the determination of the ground-based wave frequency and azimuth direction of the IGW propagation in the atmosphere has been proposed. An application of the developed method to the radiosonde measurements, conducted 28 February 2007, has given the possibility to establish that the ground-based wave frequency is equal to 14.0·10–4 rad/s and it corresponds to the wave period T=1.25 hours.