scholarly journals NEW FORMS OF THE PERTURBED MOTION EQUATION

REPORTS ◽  
2020 ◽  
pp. 5-13
Author(s):  
M.Zh. Minglibayev ◽  
Ch.T. Omarov ◽  
A.T. Ibraimova
Keyword(s):  
Model Problem ◽  
Variable Mass ◽  
Initial Approximation ◽  
Motion Equation ◽  
Mutual Distance ◽  
Celestial Bodies ◽  
Gravitating Systems ◽  
Osculating Elements ◽  
Geometric Elements ◽  
Dynamic Element

Real celestial bodies are neither spherical nor solid. Celestial bodies are unsteady, in the process of evolution their masses, sizes, shapes and structures are changes. The paper considers a model problem proposed as an initial approximation for the problems of celestial mechanics of bodies with variable mass. Based on this model problem, perturbation theory methods are developed and new forms of the perturbed motion equation are obtained. The model problem as the problem of two bodies with variable mass in the presence of additional forces proportional to speed and mutual distance is a class of intermediate motions. This class of intermediate motions describes an aperiodic motion along a quasiconical section. In this paper, on the basis of this class of aperiodic motion over a quasiconical section, various new forms of the perturbed motion equation in the form of Newton's equations are obtained. Based on the known equations of perturbed motion for the osculating geometric elements p, e, , i, , in the form of the Newton equation, we obtained the equations of perturbed motion for the following system of osculating elements p, e, i, , , and a, e, i, , , . Oscillating variables involving a dynamic element are suitable in the general case. A system of variables, where instead of the dynamic element is introduced - the average longitude in orbit is used in the quasielliptic case . The obtained new forms of the equation of perturbed motion, in the form of Newton's equations, in various systems of osculating variables can be effectively used in the study of the dynamics of non-stationary gravitating systems.

TRANSLATIONAL-ROTATIONAL MOTION OF THE TRIAXIAL BODY WITH VARIABLE COMPRESSIONS IN THE PRESENCE OF REACTIVE FORCES AND MOMENTS

2020 ◽  
Vol 69 (1) ◽  
pp. 241-246
Author(s):  
M.Zh. Minglibayev ◽  
◽  
O.B. Baisbayeva ◽  
Keyword(s):  
Coordinate System ◽  
Rotational Motion ◽  
Variable Mass ◽  
Spherical Body ◽  
Relative Orientation ◽  
The Body ◽  
Variable Size ◽  
Osculating Elements ◽  
Dynamic Shape ◽  
Central Gravitational Field

In this paper we investigated the translational-rotational motion of a triaxial body of constant dynamic shape and variable mass and size in a non-stationary Newtonian central gravitational field. Differential equations of the translationalrotational motion of the triaxial non-stationary body in the relative coordinate system with the origin at the center of a non-stationary spherical body are derived. The axes of the own coordinate system of the non-stationary triaxial body are directed along the principle axes of inertia of the body and we assumed that in the course of evolution their relative orientation remains unchanged. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is given. In the presence of reactive forces and moments the equations of translational-rotational motion of a triaxial non-stationary body in osculating elements are obtained in the presence of reactive forces and moments.

scholarly journals INVESTIGATION OF THE EVOLUTION EQUATIONS OF THE AXISYMMETRIC BODY WITH

2020 ◽  
Vol 69 (1) ◽  
pp. 247-252
Author(s):  
M.Zh. Minglibayev ◽  
◽  
S.B. Bizhanova ◽  
Keyword(s):  
Coordinate System ◽  
Rotational Motion ◽  
Evolution Equations ◽  
Second Harmonic ◽  
Variable Mass ◽  
Dynamic Structure ◽  
Approximate Expression ◽  
Axisymmetric Body ◽  
Osculating Elements ◽  
Two Bodies

In this article we consider mutually gravitating non-stationary two bodies: first body is «central», it is a sphere with a spherical density distribution, the second body is «satellite», which has an axisymmetric dynamic structure and form. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. The differential equation of translational-rotational motion of the axisymmetric body is derived with variable mass and variable size in a relative coordinate system. The axes of the own coordinate system for nonstationary two bodies coincides with the main axes of inertia and this position remains unchanged during evolution. The mass of bodies are varied isotropically in the different rates. The problem is investigated by methods perturbation theory. The equations of secular perturbations of translational-rotational motion of satellite are deduced in the analogues osculating elements Delaunay-Andoyer. The solutions of the differential equations of the perturbed motion are obtained by the numerical method and the graphs are constructed using the Wolfram Mathematica package.

scholarly journals Analytical Theory of A Trapping. In A Two-Body Problem of Variable Mass

1983 ◽  
Vol 74 ◽  
pp. 369-375
Author(s):  
T.B. Omarov ◽  
M.J. Minglibaev
Keyword(s):  
Body Problem ◽  
Model Problem ◽  
Variable Mass ◽  
Analytical Theory ◽  
Two Body Problem ◽  
Nonstationary Model ◽  
Temporal Derivative

SummaryThe new nonstationary model problem is considered. Its solution generalizes by form the known particular Mestschersky-Vinti solution in a two-body problem of variable mass. The equations of the corresponding perturbed motion are deduced. In the case of a two-body problem of variable mass μ. the perturbing force is proportional to second temporal derivative from the value μ-1 . It is possible to describe with a good approximation such qualitative effects in this problem as a trapping and disintegration on a basis of properties of the model problem. Let us consider the example of a trapping.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

Criteria for evaluation of the coordinate measurements quality of parts geometric parameters at pilot-experimental production

2019 ◽  
pp. 3-8
Author(s):  
N.Yu. Bobrovskaya ◽  
M.F. Danilov
Keyword(s):  
Quality Indicators ◽  
Quality Management System ◽  
Technical Specification ◽  
Experimental Production ◽  
Technological Heredity ◽  
Coordinate Measurements ◽  
Reasonable Choice ◽  
The Stability ◽  
Geometric Elements

The criteria of the coordinate measurements quality at pilot-experimental production based on contemporary methods of quality management system and traditional methods of the measurements quality in Metrology are considered. As an additional criterion for quality of measurements, their duration is proposed. Analyzing the problem of assessing the quality of measurements, the authors pay particular attention to the role of technological heredity in the analysis of the sources of uncertainty of coordinate measurements, including not only the process of manufacturing the part, but all stages of the development of design and technological documentation. Along with such criteria as the degree of confidence in the results of measurements; the accuracy, convergence, reproducibility and speed of the results must take into account the correctness of technical specification, and such characteristics of the shape of the geometric elements to be controlled, such as flatness, roundness, cylindrical. It is noted that one of the main methods to reduce the uncertainty of coordinate measurements is to reduce the uncertainty in the initial data and measurement conditions, as well as to increase the stability of the tasks due to the reasonable choice of the basic geometric elements (measuring bases) of the part. A prerequisite for obtaining reliable quality indicators is a quantitative assessment of the conditions and organization of the measurement process. To plan and normalize the time of measurements, the authors propose to use analytical formulas, on the basis of which it is possible to perform quantitative analysis and optimization of quality indicators, including the speed of measurements.

PROGRAM TRAINING PENGEMBANGAN KEWIRAUSAHAAN UNTUK MENINGKATKAN KEMAMPUAN PENGELOLAAN BISNIS USAHA KECIL DAN MENENGAH (UKM)

SIGMA TEKNIKA ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 57
Author(s):  
Zaenal Arifin
Keyword(s):  
Model Problem ◽  
Problem Based Learning

Berdasarkan penelitian ini tentang perlunya program pelatihan kewirausahaan yang tepat Untuk UKM, terutama bagi UKM yang lagi merintis ushanya, penelitian ini bertujuan untuk memperoleh serta mengembangkan yang tepat  program pelatihan kewirausahaan untuk meningkatkan kemampuan manajemen bisnis di kalangan UKM. Model pendekatan yang digunakan dalam penelitian ini adalah; 1) model pengembangan ilmu dan teknologi pelatihan untuk Kewirausahaan, 2) model Problem Based Learning (PBL) adalah salah satu pelatihan strategi berorientasi proses pengajaran dan pembelajaran kontekstual (CTL). Konsep pelatihan CTL membantu pelatih / instruktur / guru untuk menghubungkan materi dengan situasi dunia nyata dan juga mendorong para peserta menggunakan pengetahuan mereka untuk diterapkan dalam situasi kehidupan nyata mereka para anggota masyarakat. Dari hasil implementasi model pelatihan, dapat disimpulkan bahwa: 1) Pelatihan memadukan model Problem Based Learning (PBL) dan pengembangan sains dan program pelatihan teknologi untuk Kewirausahaan dapat diterapkan secara efektif dalam suatu program pelatihan kewirausahaan untuk UKM pemula, 2) Program ini berhasil mensinergikan materi / teori pelatihan untuk situasi dunia nyata; 3) Program  ini juga berfungsi untuk membangun kerja sama tim. Akhirnya, model ini berhasil menunjukkan efektivitasnya dengan tingkat kehadiran di 90%, serta kerja tim terbentuk dalam membuat inovatif, asli dan layak untuk menjadi mengimplementasikan proposal bisnis

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