Simplified Flat Coordinate Model for Northern Parts of Arabian Gulf

The method of coordinate conversion is still considered important and laborious due to the shift from the spatial ellipsoidal (geographic) to the flat planned system. The most common method uses a contiguous UTM system as one of the most reliable systems in the conversion process; however, this system faces a problem in large areas that contain more than one zone. The goal of this research is to create a simple and low computational cost model to represent a non-contiguous semi-UTM geographic coordinates for confined regions of the globe. The considered region taken in this study is the northern parts of Arabian Gulf (including parts of Iraq, Kuwait, Iran, and Saudi Arabia). The determined mathematical model was based on using two dimensional Taylor sequence. The most accurate representation met in this study was based on the 6th two dimensional polynomial. The estimation of equations’ coefficients was done using the least square criterion for the overall error of estimating coordinate values of either (latitude, longitude) or (Easting, Northing). The two basic determinations were applied for the forward and the backward; in the first step, the conversion of coordinates was calculated from the ellipsoidal coordinates (i.e., Longitude, Latitude) to UTM (WGS84) coordinates (i.e., Easting, Northing) and vice versa. The attained results indicated that the mathematical model used is successful for achieving the conversion process. With the use of the 6th order 2D-polynomial equations, a very small error of less than 1 m was achieved in the Easting and Northing coordinates.

EXPERIMENTAL RESEARCH OF THE ACCURACY OF NAVIGATION GNSS - RECEIVERS IN CONDITIONS OF THE CONSTRUCTED TERRITORY

Use of digital geodetic support technologies with the use of GNSS satellite systems in combination with electronic geodetic instruments, introduction of new methods of construction of geodetic networks, collection of information by ground and aerospace surveying, unification of exchange formats of measurement results based on computer technologies and their application conditions. Substantiation and development of remote methods of spatial information collection requires analysis and consideration of a number of errors in order to improve accuracy. Wikimapia is a map project for shared use with open content, which aims to identify all geographical objects with the introduction of useful information about them. It combines an interactive web map and a Wiki system. One of the features of the Wikimapia resource is that it is possible to determine geographical coordinates. To do this, you need to move the cross cursor on the object of interest and get its coordinates visually. The purpose of the study was to determine the accuracy of the coordinates of GPS receivers Garmin Oregon 450 in the built-up area, using as a basis for calibration, the resource "Wikimapia". In order to determine the accuracy of the location with the help of GARMIN Oregon 450 GPS receivers, GNSS measurements were performed at 30 marker points. Ellipsoidal coordinates were recalculated into spatial rectangles according to known formulas. In order to assess the accuracy of determining the location of marker points, the differences in the coordinates of their position were found and the root mean square error from a number of measurements was found. The average error of coordinate measurements was ± 4.79 m for the GPS receiver. Based on experimental research, the possibility of using the resource "Wikimapia" not only to quickly determine the coordinates of topographic objects, determine their categories, but also with sufficient accuracy to apply for the calibration of navigation GNSS receivers when there is no network of geodetic points. A promising direction in the process of scientific and practical research should be the creation of a general mathematical model for predicting the influence of the plurality on the location and improvement of navigation aids.

RESULTS OF BUILDING A LOCAL QUASIGEOID MODEL ON THE TERRITORY OF THE GEODETIC TRAINING GROUND OF SSUGT

The results of building a local quasigeoid model by various methods on the territory of the geodesic training ground of SSUGT, based on the data of geometric leveling, GNSS measurements, gravimetry and astronomical measurements, are presented. The advantages of using a two-dimensional model of a quasigeoid in ellipsoidal coordinates over the "flat model" of height calibration widely used in GNSS technologies are shown. The criteria for choosing a method for building a quasigeoid model on a local territory and criteria for evaluating the quality of the results are determined. The results of determining the deviations of the vertical line in a given area, with control according to astronomo-geodesic measurements, are presented. In particular, a method for quick determining the deviations of a vertical line from the differences in astronomical and geodetic zenith distances was tested. A conclusion about the best method for determining the parameters of the local model of the quasigeoid and the deviations of the vertical line for a given territory is made. The results of the research are of practical significance for the training of students and specialists in the field of geodesy.

Monitoring of spatial data coordinate basis integrity using coordinate transformations

The modern spatial data coordinate basis (SDCB) is built taking into account the variety of existing and used today geodetic networks, models of physical fields of the Earth, cartographic models, as well as coordinate systems (СS). One of the requirements for SDCB from the standpoint of system analysis is the requirement of integrity, which presupposes the unity of the determination of coordinates, that is, the consistency of the results of determining the coordinates of the same points in different CSs. The article is devoted to the monitoring of the accuracy characteristics of the available software for coordinate transformations in terms of single-stage and multi-stage transitions between ellipsoidal coordinates of different systems.

Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates.

Scattering functions of carved-ellipsoid-shaped particles

Motivated by the enriched topologies from the newly discovered nano-scaled molecular clusters, custom carved-ellipsoid models are built and their scattering functions are explored. The scattering functions of these models are derived in ellipsoidal coordinates. The theoretical scattering curves of these models can be further obtained through numerical calculation. These models have been successfully applied to the fitting of experimental scattering curves of some so-called wheel-shaped metal oxide molecular clusters.

Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid

In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new numerical method of converting Cartesian to ellipsoidal coordinates of a point on a triaxial ellipsoid are presented. An extensive test set for the coordinate conversion is used, in order to evaluate the performance of the two methods. The direct geodesic problem on a triaxial ellipsoid is described as an initial value problem and is solved numerically in Cartesian coordinates. The solution provides the Cartesian coordinates and the angle between the line of constant λ and the geodesic, at any point along the geodesic. Also, the Liouville constant is computed at any point along the geodesic, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to demonstrate the validity of the numerical method for the geodesic problem. We conclude that a complete, stable and precise solution of the problem is accomplished.

STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES

This paper presents the quasi-stationary Stefan problem in symmetric electrical contacts.The method of the solution can be obtained from the suggestion that the identity of equipotential and isothermal surfaces in contacts, which is correct for stationary fields in linear case, keeps safe for non-linear case as well. The idea is,transform the system of problem which is given in cylindrical coordinates into ellipsoidal coordinates.The analytical solution of stationary Stefan problem is found. Based on that decision was constructed the temperature profile to the approximate solution of heat problem with Joule heating in ellipsoidal coordinates. Keywords: quasi-stationary model, Stefan problem, integral method.

Note on constants of motion in conformal mechanics associated with near horizon extremal Myers–Perry black holes

We investigate dynamics of probe particles moving in the near-horizon limit of (2N + 1)-dimensional extremal Myers–Perry black hole (in the cases of N = 3, 4, 5) with arbitrary rotation parameters. Very recently it has been shown in [T. Hakobyan, A. Nersessian and M. M. Sheikh-Jabbari, Phys. Lett. B 772, 586 (2017)] that in the most general cases with non-equal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. We wrote down the explicit expressions of Liouville integrals of motion, given in the above-mentioned reference in ellipsoidal coordinates, in initial “Cartesian” coordinates in seven, nine and eleven dimensions, and found that these expressions hold in any dimension. Then, taking the limit where all of the rotational parameters are equal, we reveal that each of these N − 1 integrals of motion results in the Hamiltonian of the spherical mechanics of a (2N + 1)-dimensional MP black hole with equal nonvanishing rotational parameters.