A Semianalytical Method for Constructing Nearly Equatorial Orbits of Hypothetical Satellites of Asteroids with an Almost Spheroidal Shape

2019 ◽  
Vol 53 (2) ◽  
pp. 116-123
Author(s):  
M. A. Vashkov’yak
1999 ◽  
Vol 122 (3) ◽  
pp. 313-317 ◽  
Author(s):  
A. M. Farag ◽  
A. S. Ashour

The main purpose of this paper is to develop a fast converging semianalytical method for assessing the vibration effect on thin orthotropic skew (or parallelogram/oblique) plates. Since the geometry of the skew plate is not helpful in the mathematical treatments, the analysis is often performed by more complicated and laborious methods. A successive conjunction of the Kantorovich method and the transition matrix is exploited herein to develop a new modification of the finite strip method to reduce the complexity of the problem. The displacement function is expressed as the product of a basic trigonometric series function in the longitudinal direction and an unknown function that has to be determined in the other direction. Using the new transition matrix, after necessary simplification and the satisfaction of the boundary conditions, yields a set of simultaneous equations that leads to the characteristic matrix of vibration. The influence of the skew angle, the aspect ratio, the properties of orthotropy, and the prescribed boundary conditions are investigated. Convergence of the solution is investigated and the accuracy of the results is compared with that available from other numerical methods. The numerical results show that the convergence is rapidly deduced and the comparisons agree very well with known results. [S0739-3717(00)00202-6]


2018 ◽  
Vol 346 (12) ◽  
pp. 1123-1135
Author(s):  
Katell Derrien ◽  
Léo Morin ◽  
Pierre Gilormini

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Muhammad Asim Khan ◽  
Shafiq Ullah ◽  
Norhashidah Hj. Mohd Ali

The objective of this paper is to obtain an approximate solution for some well-known linear and nonlinear two-point boundary value problems. For this purpose, a semianalytical method known as optimal homotopy asymptotic method (OHAM) is used. Moreover, optimal homotopy asymptotic method does not involve any discretization, linearization, or small perturbations and that is why it reduces the computations a lot. OHAM results show the effectiveness and reliability of OHAM for application to two-point boundary value problems. The obtained results are compared to the exact solutions and homotopy perturbation method (HPM).


Author(s):  
F.A. Kipriyanov ◽  
◽  
Yu.A. Plotnikova ◽  

he use of vibration transport in agricultural production plays a very significant part. Vibratory conveyors have the variety of advantages over traditional transporting ma-chines such as auger and belt type conveyors used at agri-cultural enterprises for transporting mainly loose and granular materials. A rather low wear coefficient of trans-porting body itself - a conveying trough of a vibration-transporting machine may be referred to the advantages, besides, in some constructions of vibration-transporting machines the amount of friction couples is reduced to a minimum. In the design of constructions of vibration-transporting machines a question arises about the determi-nation of motion mode of particles of the transporting mate-rial. Thus, the detection of a predominant component of motion will allow forecasting the wear rate of a transporting surface and the possibility of enlarging the field of techno-logical use of vibration-transporting machines. During the research process for the determination of motion mode of grain material the shape of which was close to spheroid and ellipsoid, the method of mathematical modeling was applied. The system of differential equations of second order was compiled and solved. In the equations the influ-ence of vibration of a transporting surface on the motion of an elliptically shaped body was taken into account. To solve the system the classical method - Runge-Kutta method of the fourth order was used. The program devel-oped in programming language Python allowed identifying the motion mode of the bodies of spheroidal and ellipsoidal shapes on a vibrating surface. As the result, it was deter-mined that the motion of a body of a spheroidal shape on a vibrating surface was possible due to rolling, and the mo-tion of a body of an ellipsoidal shape was achieved be-cause of its sliding on the surface, what follows from wan-ing rotating movements. The suggested method for the determination of motion mode of a body on a vibrating sur-face is rather flexible and may be applied in calculation for larger bodies in comparison with grain seeds.


2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Indranil Ghosh ◽  
M. S. H. Chowdhury ◽  
Suazlan Mt Aznam ◽  
M. M. Rashid

Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. The main feature of the NIM is that the procedure is very simple, and it does not need to calculate any special type of polynomial or multipliers such as Adomian polynomials and Lagrange’s multipliers. Comparisons with the Adomian decomposition method (ADM) and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the NIM is a powerful alternative for differential equations providing more realistic series solutions that converge very rapidly in real physical problems.


2019 ◽  
Vol 287 ◽  
pp. 24-29
Author(s):  
Sarum Boonmee ◽  
Kittirat Worakhut ◽  
Auttachai Utsajai ◽  
Nupol Mai-Ngam ◽  
Suphalerk Rassamipat

Morphology of graphite affects the mechanical and physical properties of cast irons. It is known that the spheroidal shape of graphite promotes both tensile strength and ductility. The morphology of graphite is generally quantified by the percent nodularity and/or graphite shape factors (e.g. roundness, sphericity, compactness, aspect ratio). From the quality control aspect, the nodularity is controlled by the residual magnesium content determined by the Optical Emission Spectrometry (OES). However, the nodularity is also affected by the cooling rate and the sulfur level. Therefore, the percent nodularity alone cannot be precisely predicted by the residual magnesium. In this study, the Thermal Analysis (TA) was used to predict the residual magnesium and the nodularity of ductile iron. The newly created TA demonstrated the reliable prediction as the effect of the residual magnesium, sulfur level and the cooling rate were combined in forms of cooling curves. The correlations of the residual magnesium, the Maximum Cooling Rate (MCR) and the angle of the cooling rate curve (θ) at the end of solidification were shown in this work. Finally, the relationships were used to encode in the software for the on-site prediction.


2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Lei Wang ◽  
Wenzhong Wang ◽  
Hui Wang ◽  
Tianbao Ma ◽  
Yuanzhong Hu

A numerical analysis on the factors affecting the hydrodynamic performance for parallel surfaces with microtextures is presented in this paper. The semianalytical method and fast Fourier transform technique are implemented in the analysis. The numerical procedure is validated by comparing the results from the present model with the analytical solutions for the lubrication problem in an infinitewide sliding bearing with step-shaped textures. The numerical results show that the hydrodynamic performance can be greatly affected by the factors, such as the boundary conditions, cavitation pressure, microtextures, surface deformation, etc. This study can be of a great help for better understanding the mechanism of hydrodynamic pressure generated between parallel surfaces and realistically evaluating the improvement of tribological performance caused by textures.


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