Functional Representation of Nonlinear Systems, Interpolation and Lagrange Expansion for Functionals

1966 ◽  
Vol 88 (2) ◽  
pp. 429-436 ◽  
Author(s):  
D. Gorman ◽  
J. Zaborszky
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Initial Conditions ◽  
Analytic Representation ◽  
Input Output ◽  
The Third ◽  
Functional Representation ◽  
Lagrange Expansion ◽  
Functional Representations ◽  
Measured Input

The paper consists principally of three parts. In the first, an original analytic representation is introduced for systems where differential equations are available. In the second, the structure of the functional is analyzed with nonzero initial conditions. The third introduces functional representations for systems described by past measured input-output records.

APPLICATION OF INFORMATION TECHNOLOGY FOR MODELING THE CONTROL DYNAMICS OF A NUCLEAR REACTOR ZONING ON THE VERTICAL AXIS

2021 ◽  
Vol 5 ◽  
pp. 45-56
Author(s):  
Valery Severyn ◽  
◽  
Elena Nikulina ◽  
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Control Systems ◽  
Nuclear Reactor ◽  
Initial Conditions ◽  
Control Object ◽  
Vertical Axis ◽  
Integration Methods ◽  
Systems Of Differential Equations

The structure of information technology for modeling control systems, which includes a block of systems models, a module of integration methods and other program elements, is considered. To analyze the dynamics of control of a nuclear reactor, programs of mathematical models of a WWER-1000 nuclear reactor of the V-320 series and its control systems in the form of nonlinear systems of differential equations in the Cauchy form have been developed. For the integration of nonlinear systems of differential equations, an algorithm of the system method of the first degree is presented. A mathematical model of a WWER-1000 reactor as a control object with division into zones along the vertical axis in relative variables of state is considered, the values of the constant parameters of the model and the initial conditions corresponding to the nominal mode are given. Using information technology for ten zones of the reactor, the system integration method was used to simulate the dynamics of control of a nuclear reactor. Graphs of neutron and thermal processes in the reactor core, as well as changes in the axial offset when the reactor load is dumped under the influence of the movement of absorbing rods and an increase in the concentration of boric acid, are plotted. The analysis of dynamic processes of reactor control is carried out. The programs of integration methods and models of the WWER-1000 reactor of the V-320 series are included in the information technology to optimize the maneuvering modes of the reactor.

scholarly journals MATHEMATICAL DESCRIPTION OF THE NON-STATIONARY PROBLEM OF WORK OF THE BULLDOZER-LOADER IN THE MODE OF TURNING THE EXTENDED PARTS OF THE TELESCOPIC PUSHING BARS

2019 ◽  
pp. 577-585
Author(s):  
K. Isakov ◽  
K.T. Osmonov ◽  
T. Toktakunov
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
High Altitude ◽  
Numerical Integration ◽  
Mathematical Description ◽  
Initial Conditions ◽  
Stationary Problem ◽  
Multi Stage ◽  
Functional Mechanisms

The article examines the proposed modes of work of the project being developed to create a bulldozer-loader, adapted for more efficient maintenance, repair and construction of high-altitude and other roads. Mathematical models are proposed that describe multi-stage successive movements of one or more functional mechanisms corresponding to different modes of work. Nonlinear systems of ordinary differential equations of the second order with initial conditions, for numerical integration of which the Adams method is used, are presented.

scholarly journals THEORETICAL STUDY OF THE PROBLEM OF DEVELOPING A LOADER-LOADER WITH A TRANSFORMABLE WORKING BODY FOR THE MAINTENANCE, REPAIR OF HIGH ALTITUDE ROADS

2019 ◽  
pp. 586-593
Author(s):  
K. Isakov ◽  
K.T. Osmonov ◽  
T. Toktakunov
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
High Altitude ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Theoretical Study ◽  
Initial Conditions ◽  
Multi Stage ◽  
Functional Mechanisms

The article examines the proposed modes of work of the project being developed to create a bulldozer-loader, adapted for more efficient maintenance, repair and construction of high-altitude and other roads. Mathematical models are proposed that describe multi-stage successive movements of one or more functional mechanisms corresponding to different modes of work. Nonlinear systems of ordinary differential equations of the second order with initial conditions, for numerical integration of which the Adams method is used, are presented.

A Hierarchical Material Flow Based Automated Functional Decomposition for Conceptual Design of Working Machines

2014 ◽  
Author(s):  
Lin Yuan ◽  
Yusheng Liu
Keyword(s):  
Conceptual Design ◽  
Material Flow ◽  
Transformation Model ◽  
Input Output ◽  
Primary Input ◽  
Functional Decomposition ◽  
Functional Representation ◽  
Operation Process ◽  
Internal Structures ◽  
Functional Representations

The purpose of conceptual design is to build the function structure and find the principle solution for fulfilling it. A formal functional representation is needed for decomposing the overall function to sub-functions with the computer-aid reasoning process. However, the existing functional representations lack of supporting the description of attributes and internal structures of input/output material flows. Material flow may be much more complicated than the other two kinds of flows (signal flow and energy flow) since its geometry and topology may be very complex, and which hinders the automated functional decomposition. In this paper, we propose a hierarchical material representation for the working machines which use material as the primary input/output flows. We combine input/output transformation model with “verb+noun” pairs, using the standard vocabulary of functional basis, to model function formally and objectively. Therefore, the functional effects can be inferred from the information contained in flows. Moreover, we propose the concept of action as an operation process that bridge what and how of one function to guide the further decomposition. Finally, a prototype tool is developed as a MagicDraw’s plug-in to implement the decomposition process.

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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