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View article: Geodynamic shape evolution and inhomogeneous distribution of the Earth’s density
Geodynamic shape evolution and inhomogeneous distribution of the Earth’s density Open
The paper presents the results and their interpretation in the study of planetary distributions of density and energy in an ellipsoidal planet under an additional condition — the minimum gravitational energy of the Earth. Also, the compone…
View article: Representationofcubicirrationalityusingthesumoftwoperiodicbranchedchainfractions
Representationofcubicirrationalityusingthesumoftwoperiodicbranchedchainfractions Open
The paper creates such an algorithm that represents cubic irrationality using the sum of two periodic branched chain fractions. Theunity and convergence of these fractions are proved. It is logically assumed that the irrationalities of hig…
View article: Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet
Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet Open
This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential. The primary focus lies in const…
View article: About metric and angular dependencies of spatial straight line notches and their use in engineering and geodetic works
About metric and angular dependencies of spatial straight line notches and their use in engineering and geodetic works Open
In applied geodesy tasks, it may be necessary to determine spatial angles. When bringing a 3D design of buildings and structures to the field with the help of an electronic total station (ES), it is important to verify the spatial angles b…
View article: Features of determining the real property valuation using the alternative approach of matrix pseudo-inversion
Features of determining the real property valuation using the alternative approach of matrix pseudo-inversion Open
The purpose of the work is the application of using the method of matrix pseudo-inversion to determine the market value of real estate objects using the mathematical apparatus of the method of comparing sales of similar real estate objects…
View article: Gravity potential and its component of centrifugal force inside the ellipsoidal planet
Gravity potential and its component of centrifugal force inside the ellipsoidal planet Open
A method for determining the gravitational potential of a celestial body whose surface is a sphere or ellipsoid with an abrupt mass distribution function is proposed. For these cases, the formulas for determining the internal potential and…
View article: Investigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks
Investigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks Open
The paper considers representations of the Earth external gravitational field, supplementing its traditional approximation by series in spherical functions. The necessity for additional means of describing the external potential is dictate…
View article: Nonlinear method for determining external orientation elements of digital images obtained from drone
Nonlinear method for determining external orientation elements of digital images obtained from drone Open
We have suggested the method of application of a direct solving of the systems of nonlinear equations for finding the elements of external orientation (EEO) to perform aerial photography by unmanned aerial vehicles (UAVs). The elements of …
View article: The gradient construction approach analysis of the three-dimensional mass distribution function of the ellipsoidal planet
The gradient construction approach analysis of the three-dimensional mass distribution function of the ellipsoidal planet Open
Purpose. To investigate the features of the algorithm implementation for finding the derivatives of the spatial distribution function of the planet's masses with the use of high-order Stokes constants and, on the basis of this, to find its…
View article: Results of the software application for determination elements of external orientation of digital images of topographic aerial surveying from UAV
Results of the software application for determination elements of external orientation of digital images of topographic aerial surveying from UAV Open
One of the problems with the use of UAVs for high-precision mapping is the inability to install on these devices an accurate stabilization system to determine the angular EEO images, so there is a need to develop methods for accurate locat…
View article: On some properties of determinants with complex elements and their practical application
On some properties of determinants with complex elements and their practical application Open
The formulas presented in this paper make it possible to select the real and imaginary part of the determinant value of the n -th order complex quantity, greatly simplifying the process of its deployment. Moreover, its module is given by t…
View article: Influence of the principle of minimum potential energy on the distribution of density and gravitational energy of the Earth for the reference model PREM
Influence of the principle of minimum potential energy on the distribution of density and gravitational energy of the Earth for the reference model PREM Open
From the point of view of modeling the internal structure of the Earth, its figure and evolution play an important role, which to one degree or another are associated with gravitational energy and the principle of its minimization. The rea…
View article: On approach to determine the internal potential and gravitational energy of ellipsoid
On approach to determine the internal potential and gravitational energy of ellipsoid Open
Formulas are derived for the calculation of the potential of bodies, which surface is a sphere or an ellipsoid, and the distribution function has a special form: a piecewise continuous one-dimensional function and a three-dimensional mass …
View article: GEODYNAMICS
GEODYNAMICS Open
Purpose. To create an algorithm for constructing a three-dimensional masses distribution function of the planet and its derivatives taking into account the Stokes constants of arbitrary orders. Being based on this method, the task is to pe…
View article: Web-mapping of environmental pollution of the surface waters of the Lviv region
Web-mapping of environmental pollution of the surface waters of the Lviv region Open
The ecological status of the surface waters of the Lviv region is influenced by closely related various factors, namely: soil pollution, atmosphere, change of landscape structure and technogenic congestion of the territory, inefficient wor…
View article: Estimation of accuracy of the values defined from functional dependencies
Estimation of accuracy of the values defined from functional dependencies Open
The generalization of the formula of a priori accuracy estimation for the case of implicitly given functions is performed. This is based on the classical definition of the root mean square error, which is given as the sum of the squares of…
View article: On representation of the internal spherical functions and their derivatives in the planetary coordinate system
On representation of the internal spherical functions and their derivatives in the planetary coordinate system Open
The expressions of spherical functions and their derivatives in a Cartesian coordinate system are obtained.In opposite to the representation of polynomials in a spherical coordinate system, the derived recurrence relations make it possible…
View article: GEODYNAMICS
GEODYNAMICS Open
Purpose.Parameters of Earth's gravitational field ( , , nk С , nk S ) are determinated by its figure and internal filling (mass distribution) that have a different influence on their formation.Using a well-known representation of the plane…
View article: The accuracy investigation of point coordinates’ determination using a fixed basis for high-precision geodesy binding
The accuracy investigation of point coordinates’ determination using a fixed basis for high-precision geodesy binding Open
Modern scanners can perform terrestrial topographic survey with resolution of 1 cm and accuracy of 2 mm in just a few minute‘s time, from the distance of up to 100 meters. However, for surface topographical surveying of large territories o…
View article: Method of construction of three-dimensional mass distribution of hydrostatically introduced ellipsoidal planet
Method of construction of three-dimensional mass distribution of hydrostatically introduced ellipsoidal planet Open
Formulas and relations for the realization of the method of construction of three-dimensional mass distribution of hydrostatically balanced ellipsoidal planet are derived. First, it is possible to interpret the anomalies of the external gr…
View article: DETERMINATION OF THE SHORTEST DISTANCE AND ANGLE BETWEEN THE NORMAL TO THE ELLIPSOID OF ROTATION BY COORDINATES OF POINTS GNSS OBSERVATIONS
DETERMINATION OF THE SHORTEST DISTANCE AND ANGLE BETWEEN THE NORMAL TO THE ELLIPSOID OF ROTATION BY COORDINATES OF POINTS GNSS OBSERVATIONS Open
Національний університет «Львівська політехніка» ВИЗНАЧЕННЯ НАЙКОРОТШОЇ ВІДСТАНІ ТА КУТА МІЖ НОРМАЛЯМИ ДО ЕЛІПСОЇДА ОБЕРТАННЯ ЗА КООРДИНАТАМИ ПУНКТІВ GNSS-СПОСТЕРЕЖЕНЬАнотація.У даній роботі представлено методику визначення
View article: The algorithm and the basic formulas of the reduction of fundamental constants to the planetary coordinate system
The algorithm and the basic formulas of the reduction of fundamental constants to the planetary coordinate system Open
In this article one of the algorithms for the construction of parameters of the planet gravitational field and its dynamical ellipticity into a planetary coordinate system is presented. The example shows the possibility of its application …
View article: Research of structure of coefficients' representation of the potential by everywhere convergent series
Research of structure of coefficients' representation of the potential by everywhere convergent series Open
This paper offers the representation of the potential of planets by a sequence of non-harmonic continuous functions, which are determined by direct resolve of the inversion radius in the binomial series. The coefficients of such interpreta…
View article: GEODYNAMICS
GEODYNAMICS Open
Purpose.To build a three-dimensional function of the mass distribution of the Earth's interior according to the parameters (Stokes constant to the second order inclusive) of the external gravitational field of the Earth without considering…