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.

MHD Hybrid Cu-Al2O3/ Water Nanofluid Flow with Thermal Radiation and Partial Slip Past a Permeable Stretching Surface: Analytical Solution

The influence of velocity slip and thermal radiation effects on the magnetohydrodynamic hybrid Cu-Al2O3/water nanofluid flow over a permeable stretching sheet is reported in this paper. The similarity transformation is adopted to reduce the partial differential equations to the ordinary differential equations. Exact analytical method is implemented to solve the problem. Maple program is used to facilitate the calculation process. The new additional effects which are the velocity slip and thermal radiation effects are considered towards the model to scrutinize the impacts. The effects of various parameters towards the velocity and temperature profiles are demonstrated through graphs, meanwhile the skin friction coefficient and the local Nusselt number are exhibited through the tabulation of data. The existence of velocity slip reduced the velocity profile but enhanced the temperature profile. The thermal radiation effect has increased the temperature profile. The heat transfer rate are enhanced for the case of hybrid nanofluid compared to the mono nanofluid.

An algorithm to solve the inverse kinematics to a stewart platform

Mechanical systems in motion type parallel structures are solid, fast and accurate. Between mobile systems parallel the best known and used system is that of a Stewart platform, as being and the oldest system, quickly, solid and accurate. The paper presents a few main elements of the Stewart platforms. In the case where a motto element consists of a structure composed of two elements in a relative movement from the point of view of the train of propulsion and especially in the dynamic calculations, it is more convenient to represent the motto element as a single moving item. The paper presents an exact, original analytical geometry method for determining the kinematic and dynamic parameters of a parallel mobile structure. Compared with other methods already known, the presented method has the great advantage of being an exact analytical method of calculation and not one iterative-approximately.

MORPHOLOGICAL MOMENTS OF BINARY IMAGES

The concept of morphological moments of binary images is introduced. Morphological moments can be used as a shape descriptor combining an integral width description of an object with a description of its spatial distribution. The relationship between the proposed descriptor and the disc cover of the figure is discussed and an exact analytical method for descriptor calculation is proposed within the continuous morphology framework. The approach is based on the approximation of the shape by a polygonal figure and the extraction of its medial representation in the form of the continuous skeleton and the radial function. The proposed method for calculation of morphological moments achieves high accuracy and it is computationally efficient. Experimentations have been conducted. Obtained results indicate that the morphological moments are a more informative and rich shape descriptor than the area of the disc cover. Application of morphological moments to the font recognition task improves the recognition quality.

An Exact Analytical Approach for Free Vibration Analysis of Built-Up Space Frames

Coupled in- and out-of-plane bending, axial, and torsional vibrations exist in a built-up space frame, which greatly challenges the conventional modal approach. A wave-based exact analytical method is applied to study vibrations in built-up multistory space frames. From the wave vibration standpoint, vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Free vibration responses are studied based on classical vibration theories. Numerical examples are given with comparison to results available in the literature. Good agreements have been reached. This study not only provides an exact analytical approach to complex vibration problems in built-up multistory space frames that have mostly been studied numerically but also provides a benchmark to existing numerical tools.