On making problems evolutionarily friendly part 2: Evolving the most convenient coordinate systems within which to pose (and solve) the given problem

1998 ◽  
pp. 281-290 ◽  
Author(s):  
A. V. Sebald ◽  
K. Chellapilla
Keyword(s):  
Coordinate Systems ◽  
The Given

Requirement for Limits of Action and Wildhaber’s Limit Normal

2003 ◽  
Author(s):  
Sho Honda
Keyword(s):  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Coordinate Systems ◽  
Design Point ◽  
Tooth Surfaces ◽  
Angular Velocities ◽  
The Common ◽  
The Given ◽  
Designing Method

One of the most important criteria to design a gear pair which has smooth tooth surfaces around a given design point is how far the design point is from the limits of action. However, in the present theories, the definition is obscure and the calculation methods are not clear except for cylindrical gears. In this paper, when a path of contact and its contact normals are given according to the unified designing method applicable to all kinds of gears having the same equations defined in the common coordinate systems which are determined by the disposition of the gear axes and the angular velocities, the infinitesimal surface of action along the path of contact and the corresponding tooth surfaces are determined and the requirement for limit of action for all kinds of gears is obtained. To design a smooth tooth surface around the design point, it is convenient to look for the limit path of contact with its contact normal whose limit of action coincides with the design point, from which a design path of contact must be inclined adequately. Finally, it is shown that Wildhaber’s limit normal is the contact normal of the limit path of contact solved under the condition that the given path of contact is an arc around the gear axis and is just one solution of the limits of action of a hypoid gear pair.

scholarly journals Calculation of the Shaping of a Space Umbrella Antenna During Strong Bending of Radial Rods Connected Along Parallels by Tensile Cables

2021 ◽  
Vol 56 (5) ◽  
pp. 690-701
Author(s):  
S. V. Russkikh ◽  
F. N. Shklyarchuk
Keyword(s):  
Hydraulic Cylinder ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Regular Polygons ◽  
Coordinate Systems ◽  
Parabolic Antenna ◽  
In Series ◽  
Curved Rods ◽  
The Given ◽  
System Axis

Abstract— A cyclically symmetric umbrella antenna is considered, the frame of which consists of flexible inextensible radial rods connected in nodes along parallels by tensile cables. In the initial transport position, the multilink rods are packed in packages oriented in the direction of the system axis. After the packing ties are removed, the rods are deployed in radial planes under the action of elastic springs connecting the links, and are fixed in rectilinear positions at a given angle with respect to the axis, at which all cables connecting the same type of rod nodes take the form of regular polygons, while remaining loose. Further, under the action of the force of a damping hydraulic cylinder with pre-compressed springs, the root parts of all rods are slowly turned to the stops. In the final position, the radial rods, connected at the nodes by tensioned cables, take a curved shape. The tensile stiffnesses of the cables are determined so that the radial and axial coordinates of the nodes of the curved rods coincide with the coordinates of the points of the given surface of revolution. A model of strong bending of a flexible inextensible rod is constructed taking into account the unknown radial reactions of tensioned cables acting on it at the nodes. The links of the rod are considered as “cantilever” elements connected in series at the nodes in local coordinate systems, which can make large displacements and turns. The bending of each element is described by two specified functions, the shrinkage of the element due to bending is taken into account in a quadratic approximation. The obtained nonlinear deformation equations of the system, taking into account the geometric connections at the nodes, are solved by the method of successive approximations with respect to the unknown reactions of the cables. The obtained values of the reactions are then used to determine the required tensile stiffness of the cables at the given coordinates of the nodes. As an example of the calculation, a parabolic antenna is considered for various numbers of radial rods and components of links. The estimates of the accuracy of the proposed computational model of the antenna shaping are carried out.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

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.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

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.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

Personal Problem Solving of Partners in Divorce Proceedings

2015 ◽  
Vol 36 (1) ◽  
pp. 82-103 ◽  
Author(s):  
Tereza Soukupova ◽  
Petr Goldmann
Keyword(s):  
Gender Differences ◽  
Problem Solving ◽  
Thematic Apperception Test ◽  
Scoring Systems ◽  
Personal Control ◽  
Personality Characteristics ◽  
Personal Problem ◽  
Thematic Apperception ◽  
And Gender ◽  
The Given

Abstract. The Thematic Apperception Test is one of the most frequently administered apperceptive techniques. Formal scoring systems are helpful in evaluating story responses. TAT stories, made by 20 males and 20 females in the situation of legal divorce proceedings, were coded for detection and comparison of their personal problem solving ability. The evaluating instrument utilized was the Personal Problem Solving System-Revised (PPSS-R) as developed by G. F. Ronan. The results indicate that in relation to card 1, men more often than women saw the cause of the problem as removable. With card 6GF, women were more motivated to resolve the given problem than were men, women had a higher personal control and their stories contained more optimism compared to men’s stories. In relation to card 6BM women, more often than men, used emotions generated from the problem to orient themselves within the problem. With card 13MF, the men’s level of stress was less compared to that of the women, and men were more able to plan within the context of problem-solving. Significant differences in the examined groups were found in those cards which depicted significant gender and parental potentials. The TAT can be used to help identify personality characteristics and gender differences.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

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