Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates

Conversion between space rectangular (X, Y, Z) and curvilinear (φ, λ, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently or simultaneously equal to zero. Therefore, this study attempts to put forth an optimum coordinate conversion technique between space rectangular and curvilinear coordinates. The data used are coordinates of points which include the space rectangular coordinates and their equivalent curvilinear coordinates. They were observed and processed in Nigeria using Doppler 9 software by African Doppler Survey (ADOS) and they were confirmed to be of first order accuracy and hence of high quality. The data processing involved the design of the optimum techniques equations, coding of the algorithms and necessary computations to obtain results. Analyzing the results obtained, it can be inferred that the designed optimum model has successfully carried out the conversion between space rectangular and curvilinear coordinates. Therefore, the optimum technique model is recommended for use for the conversions from Space rectangular coordinates to Geocentric, Geodetic, Reduced coordinates and vice versa.

Zredukowane współrzędne obrysu strumienia na trapezowym progu przepuszczalnym z przelewem o ostrej krawędzi na skarpie górnej

The purpose of the work was to develop a typical shape of water surface profi le above trapezoidal gabion sill with the sharpcrested weir on the upstream slope. Reduced co-ordinates of the water surface profile above trapezoidal gabion sill with a sharp-crested weir on the upstream slope were developed. The ordinate points of the contour were reduced in relation to the height of the upstream water level above the sharp-crested weir. The cut off points of the contour were reduced according to the length of the zone influencing the stream to the inside of the stone sill. In the analyzes, the results of laboratory tests were used, according to which the shape of the free surface profile reduced coordinates was developed. The analyzed sill consisted of the permeable part filled natural aggregates and the solid part in the form of an inclined sharp-crested weir. The sill had a symetrical trapezoidal shape with the slopes of 1 : 1. The shape of the stream flowing over the analyzed sill depends on the head of the upstream water level above the crest of the slope weir. As a result of the conducted analyzes, a uniform stream shape was obtained for both the free and wave flow of the disturbance zone. The profiles obtained have strong correlation dependence. The obtained results can be taken into account during design similar hydraulic structures.

Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

STIFFNESS AND DYNAMIC ANALYSIS OF A PLANAR CLASS-2 TENSEGRITY MECHANISM

Tensegrity mechanisms have several attractive characteristics such as light-weight, deployable and easily modeled. In this paper, the stiffness and dynamics of a planar class-2 tensegrity mechanism are studied. Firstly, the solutions to the kinematic problems are found by using a method of reduced coordinates. Then, the stiffness of the mechanism is investigated on the basis of a stiffness matrix. The mechanism’s stiffnesses along directions defined nodal coordinates are computed. Finally, a dynamic model is derived and the motions of the mechanism are simulated.

One-axis molecular rotation and phonon scattering in solid C2H6 and C2F6

Using solid C2H6 and C2F6 as an example, the one-axis molecular rotation effect on thermal conductivity has been considered in orientationally-ordered (OO) and orientationally-disordered (OD) phases of simple molecular crystals. The influence of molecular rotation on the heat transfer processes has been studied by a modified method of reduced coordinates, which permitted separating phonon-phonon and phonon-rotation contributions to the total thermal resistance.