scholarly journals Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival

Author(s):  
V. V. Legkostup ◽  
V. E. Markevich

This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.

2007 ◽  
Vol 364-366 ◽  
pp. 499-503 ◽  
Author(s):  
Guo Jun Dong ◽  
Cheng Shun Han ◽  
Shen Dong

This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.


1970 ◽  
Vol 10 (04) ◽  
pp. 393-404 ◽  
Author(s):  
G.J. Hirasaki ◽  
P.M. O'Dell

Abstract For most reservoirs the reservoir thickness and dip vary with position. For such reservoirs, the use of a Cartesian coordinate system is awkward as the coordinate surfaces are planes and the finite-difference grid elements are rectangular parallepipeds. However, these reservoirs may be efficiently parallepipeds. However, these reservoirs may be efficiently modeled with a curvilinear coordinate system that has coordinate surfaces that coincide with the reservoir surfaces. A procedure is presented that may be used to determine a curvilinear coordinate system that will conform with the geometry of the reservoir. The reservoir geometry is described by the depth of the top of the reservoir and the thickness. The mass conservation equations are presented in curvilinear coordinates. The finite-difference equations differ from the usual Cartesian coordinate formulation by a factor multiplying the pore volume and transmissibilities. A numerical example is presented to illustrate the magnitude of the error that may occur in the computed oil recovery if the Cartesian coordinate system is simply modified to yield the correct depth and pore volumes. Introduction Many reservoirs have a shape that is inconvenient and possibly inaccurate to model with Cartesian coordinates. The use of a curvilinear coordinate system that follows the shape of the reservoir can be advantageous for such reservoirs. The formulation discussed here will have the greatest advantage in modeling thin reservoirs but will have little advantage in modeling a reservoir whose thickness is greater than its radius of curvature, such as a pinnacle reef. pinnacle reef. In this paper the reader is introduced to various grid systems used to model reservoirs. A brief discussion of some concepts of differential geometry contrasts differences between Cartesian coordinates and curvilinear coordinates. A curvilinear coordinate system for modeling reservoir geometry is presented. Formulation of the conservation equations in curvilinear coordinates and the necessary modifications to pore volume and transmissibility are discussed. A numerical example illustrates the magnitude of the error that may result from some coordinate systems. COORDINATE SYSTEMS AND RESERVOIR GRID NETWORKS A reservoir is usually described with the depth, thickness, boundaries, etc., shown on a structure map with sea level as a reference plane. For example, the subsea depth may be shown as a contour map on the reference plane with a Cartesian coordinate grid superimposed on the reference plane as shown on Fig. 1. The Cartesian coordinates, plane as shown on Fig. 1. The Cartesian coordinates, (y1, y2), have been defined as the coordinates for the reference plane. If the reservoir surfaces are parallel planes, Cartesian coordinates may be used. The Cartesian coordinate may be rotated such that the coordinate surfaces coincide with the reservoir surfaces. SPEJ P. 393


2017 ◽  
Vol 919 (1) ◽  
pp. 13-17
Author(s):  
G.A. Shanurov ◽  
A.D. Manilova

Inertial coordinate system and geodetic (terrestrial) coordinate system are used in processing of results of topographic survey, carried out with a mobile scanning complex. Mobile scanning complex geodetic coordinates, in turn, are presented in geodetic three-dimensional rectangular coordinate system form, in geodetic ellipsoidal coordinate system form and in the form of coordinates on a geodetic projection plane. The results of research, carried out earlier [4–7], suggest that the coordinate transformation on large areas distorts geodetic points coordinates. The article presents the results of similar investigations, but applied to a local area, limited by a mobile scanning complex surveying area. The accuracy of the mobile scanning complex coordinates is characterized by the mobile scanning complex coordinates errors cofactor matrix. It turned out that the local site sequential coordinate transformation procedure from one coordinate system to another coordinate system does not introduce any distortion into the mobile scanning complex coordinates.


2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Fangcheng Lü ◽  
Jiayi Guo ◽  
Leilei Niu ◽  
Jianghai Geng ◽  
Yirui Pan

A new three-dimensional (3D) analysis method is proposed as the existing two-dimensional (2D) method has low accuracy in analysing the vibration characteristics of oil-immersed shunt reactors, such as ultrahigh-voltage (UHV) shunt reactors. First of all, a set of 3D laminated coordinate systems was defined based on silicon steel lamination rules, in which the anisotropy of magnetic properties for laminated silicon steel in the rolling direction (RD), the transverse direction (TD), and the lamination direction (LD) were considered. Then, the mapping between laminated coordinate systems and space rectangular coordinate system was established to unify the parameters in different laminated coordinate systems. With the mapping, the anisotropy of the magnetic properties in the laminated coordinate systems was transformed into a rectangular coordinate system. Next, two sets of comparative studies between the new 3D method and the traditional 2D method were carried out, which show that the 3D method has high precision and a wide application range. Finally, the relationship between air gap number and core vibration of UHV shunt reactors was studied by the new 3D method. The results show that, as the number of air gaps increases, the magnetic flux density and the total force area of Maxwell force are increased, resulting in the intensification of core vibration. The conclusions of this paper are helpful for the design of large oil-immersed reactors.


1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.


1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.


2007 ◽  
Author(s):  
Luis N. Gonzalez Castro ◽  
Amy R. Pritchett ◽  
Daniel P. J. Bruneau ◽  
Eric N. Johnson
Keyword(s):  

Author(s):  
Andrey Dudnik

Актуальність теми дослідження. Нині безпровідні сенсорні мережі є важливим інструментом для дослідження фізичного світу. Їхня важливість пов’язана з новими можливостями використання, завдяки таким характеристикам, як відсутність необхідності в кабельній інфраструктурі, мініатюрних вузлах, низькому енергоспоживанні, вбудованому радіоінтерфейсі, досить високій потужності передачі, відносно низькій вартості. Тому існує проблема створення нових засобів, що покращили б ефективність їх використання, що б дало змогу розширити сфери застосування. Постановка проблеми. У процесі розроблення таких систем розробникам доводиться вирішувати суперечність між зниження точності вимірювання відстані, зі зростанням дальності розташування об’єктів, обмеженою потужністю передавачів і дорогою вартістю спеціальних вузлів, що отримують точні координати із супутника. Наявність цих обмежень підвищує імовірність похибок при локалізації об’єктів у безпровідних сенсорних мережах. Аналіз останніх досліджень і публікацій. Були розглянуті останні публікації у відкритому доступі, включаючи існуючі алгоритми вимірювання відстані та задачі енергоефективності передавачів. Виділення недосліджених раніше частин загальної проблеми. Підвищення точності вимірювання відстані заобів, що використовують існуючі алгоритми вимірювання відстані. Постановка завдання. Удосконалення методу вимірювання відстані пристроями безпровідних сенсорних мереж, шляхом застосування мікропроцесорних фазометрів. Виклад основного матеріалу. Локалізація об’єктів відбувається за допомогою методу TDOA (Time Difference of Arrival). Дані, що були одержані після використання цього методу, надсилаються до мікропроцесорного фазометра, який визначає період між фазами радіо- та ультразвукового сигналу, що є пропорційною величиною до відстані між об’єктами. Висновки відповідно до статті. Запропонований метод дозволяє покращити точність процесу локалізації об’єктів у безпровідних сенсорних мережах.


2020 ◽  
Vol 962 (8) ◽  
pp. 24-37
Author(s):  
V.E. Tereshchenko

The article suggests a technique for relation global kinematic reference system and local static realization of global reference system by regional continuously operated reference stations (CORS) network. On the example of regional CORS network located in the Novosibirsk Region (CORS NSO) the relation parameters of the global reference system WGS-84 and its local static realization by CORS NSO network at the epoch of fixing stations coordinates in catalog are calculated. With the realization of this technique, the main parameters to be determined are the speed of displacement one system center relativly to another and the speeds of rotation the coordinate axes of one system relatively to another, since the time evolution of most stations in the Russian Federation is not currently provided. The article shows the scale factor for relation determination of coordinate systems is not always necessary to consider. The technique described in the article also allows detecting the errors in determining the coordinates of CORS network in global coordinate system and compensate for them. A systematic error of determining and fixing the CORS NSO coordinates in global coordinate system was detected. It is noted that the main part of the error falls on the altitude component and reaches 12 cm. The proposed technique creates conditions for practical use of the advanced method Precise Point Positioning (PPP) in some regions of the Russian Federation. Also the technique will ensure consistent PPP method results with the results of the most commonly used in the Russian Federation other post-processing methods of high-precision positioning.


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