scholarly journals Symbolic-Numerical Modeling of the Influence of Damping Moments on Satellite Dynamics

2018 ◽  
Vol 173 ◽  
pp. 05008
Author(s):  
Sergey A. Gutnik ◽  
Vasily A. Sarychev
Keyword(s):  
Numerical Modeling ◽  
Asymptotic Stability ◽  
Gröbner Basis ◽  
Algebraic Equations ◽  
Grobner Basis ◽  
Real Roots ◽  
Spatial Oscillations ◽  
Damping Torque ◽  
Orbital Coordinate System

The dynamics of a satellite on a circular orbit under the influence of gravitational and active damping torques, which are proportional to the projections of the angular velocity of the satellite, is investigated. Computer algebra Gröbner basis methods for the determination of all equilibrium orientations of the satellite in the orbital coordinate system with given damping torque and given principal central moments of inertia were used. The conditions of the equilibria existence depending on three damping parameters were obtained from the analysis of the real roots of the algebraic equations spanned by the constructed Gröbner basis. Conditions of asymptotic stability of the satellite equilibria and the transition decay processes of the spatial oscillations of the satellite at different damping parameters have also been obtained.

Methods to solve algebraic equations in cryptanalysis

2010 ◽  
Vol 45 (1) ◽  
pp. 107-136 ◽  
Author(s):  
Igor Semaev ◽  
Michal Mikuš
Keyword(s):  
Gröbner Basis ◽  
Algebraic Equations ◽  
Grobner Basis ◽  
Sat Solving

ABSTRACT The goal of the present paper is a survey of methods to solve equation systems common in cryptanalysis. The methods depend on the equation representation and fall into three categories: Gröbner basis algorithms, SAT-solving methods and Agreeing-Gluing algorithms.

scholarly journals Grobner Basis Over Ideals of Multivariate Polynomial Ring: قواعد جروبنر فوق مثاليَّات الحدوديَّات بأكثر من متغير

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Khaled Suleiman Al-Akla
Keyword(s):  
Polynomial Ring ◽  
Gröbner Basis ◽  
Main Axis ◽  
Structural Approach ◽  
Algebraic Equations ◽  
Grobner Basis ◽  
Multivariate Polynomial ◽  
Multiple Variables ◽  
Definition Of

Grobner basis are considered one of the modern mathematical tools which has become of interest for the researchers in all fields of mathematics. Grobner basis are generally polynomials with multiple variables that has certain characteristics. it's includes two main axis:                                                                            1- The first axis we have presented the definition of Grobner basis and their properties. 2- The second axis we have studied some applications of Grobner basis, and we give some examples about its. The goal of these paper is to identify Grobner basis and some algorithms related to how to find them and talked about the most important applications, including: the issue of belonging and the issue of containment, and to reach our goal to follow the analytical and structural approach, we defined these basis and we have many results, The Grosvenor we obtained is not alone in general and to be single, some additional conditions must be set on these basis, and we conclude that Grobner basis have many applications in the solutions of algebraic equations in more than one transformer and in many fields.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

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