## A SOLID BODY SURFACING MATHEMATICAL MODEL IN STRATIFIED INCOMPRESSIBLE FLUID UNDER THE ACTION OF BUOYANCY FORCE AND LIMITED MOTION CONTROL

Industry 4.0, Vol. 3 (2018), Issue 3, pg(s) 109-111

This paper results are based on the mathematical model of the motion control of an autonomous solid body in stratified incompressible fluid which was presented by the authors at XII MTM Congress held in September 2015 and XIV MTM Congress held in September 2017. This paper presents an analytical mathematical model of a solid body, which surfaces in stratified viscous incompressible fluid, a difference scheme and its solution. The body is equipped with controlled rudders, wings of finite span, and does not have its own propulsion system. It is moved by the influence of the buoyancy force and wings lift effect. This body motion is considered to be planeparallel motion. The mathematical model synthesis is based on the hydrodynamic equations.

## FUNDAMENTALS OF THE KINETIC THEORY OF MULTICOMPONENT EMULSIONS

Mathematical Modeling, Vol. 1 (2017), Issue 2, pg(s) 75-79

The paper proposes a mathematical model for describing the dynamics of multicomponent emulsions, based on ideas and methods of the kinetic theory of gases. The methodological basis of the proposed theory is the ideas and methods of the theory of integral kinetic equations.

## THE NUMERICAL-ANALYTIC SUBSTANTIATION OF THE POSSIBILITY OF AUTOMATED MOTION CONTROL OF AN AUTONOMOUS RIGID BODY WITHOUT ITS OWN PROPULSION SYSTEM IN INCOMPRESSIBLE STRATIFIED VISCOUS FLUID

The report presents a mathematical model of the motion control of an autonomous solid body moving in incompressible stratified viscous fluid and analytical and numerical analysis of this model. It is assumed that the body does not have its own propulsion system, but is equipped with controlled rudders – wings of finite span. It is moved by the influence of the buoyancy force and wings lift. The control is produced by the angle of attack of the wing change for ensuring access to the given point by this solid body. This body motion is considered to be plane-parallel motion. This paper results are based on the mathematical model which was presented by the authors at XII MTM Congress held in September 2015 and XIII MTM Congress held in March 2016.

• ## THE SOLUTION OF THE SYNTHESIS PROBLEM OF PARTIAL MOTION CONTROL OF A RIGID BODY IN AN INCOMPRESSIBLE VISCOUS FLUID

The report presents an analytical and numerical analysis of mathematical model of the control synthesis of a solid body moving in an incompressible viscous fluid. It is assumed that the body does not have its own propulsion system, but is equipped with controlled rudders – wings of finite span. It pops up under the influence of the buoyancy force and wings lift. The basic mathematical model was presented by the authors at XII MTM Congress held in September 2015.

• ## «MOMENT» REPRESENTATION OF «FAST DECREASING» GENERALIZED FUNCTIONS AND THEIR APPLICATION TO SEVERAL APPLIED STOCHASTIC PROBLEMS

This paper describes the process of building special space of generalized functions, its properties and applications. Presented applications are: constructive solution of Kolmogorov-Feller type equation with polynomial drift coefficient; proof of exponential nature of equilibrium establishment in rarefied gas, described by Boltzmann equation of kinetic theory of gases.

## THE MATHEMATICAL MODEL AS A BASIS FOR THE NATURAL CLASSIFICATION OF SYSTEMS AND PROCESSES

Mathematical Modeling, Vol. 1 (2017), Issue 1, pg(s) 4-6

This paper attempts to provide a transparent and, if possible, a formal hierarchy of the main types of mathematical models used in the description of dynamic processes inside, at first glance, different systems. It is emphasized that the mathematical modeling is a natural and universal environment for effective analysis of system processes of different nature. From our point of view, the term "system analysis" means the methodology for classification of real systems (physical, biological, economic, social, etc.), which is based on the classification of mathematical models that are used to describe these systems.

## SIMPLIFIED ANALYTIC SOLUTION OF THE PROBLEM OF AUTOMATED MOTION CONTROL OF AN AUTONOMOUS RIGID BODY WITHOUT ITS OWN PROPULSION SYSTEM IN INCOMPRESSIBLE STRATIFIED VISCOUS FLUID

Industry 4.0, Vol. 2 (2017), Issue 3, pg(s) 108-110

This paper results are based on the mathematical model of the motion control of an autonomous solid body moving in incompressible stratified viscous fluid which was presented by the authors at and XIII MTM Congress held in March 2016 and XIII MTM Congress held in September 2016. It is assumed that the body does not have its own propulsion system, but is equipped with controlled rudders – wings of finite span. It is moved by the influence of the buoyancy force and wings lift effect. The control is produced by the angle of attack of the wing change for reaching to a neighborhood of the given point by this solid body. This body motion is considered to be planeparallel motion. At this paper authors present a simplification of this mathematical model in order to find an analytical solution of the differential equation describing the object motion and a necessity and acceptability analysis of the simplification.

## MATHEMATICAL MODELING AS A KEY TO SYSTEM ANALYSIS METHODOLOGY

Industry 4.0, Vol. 1 (2016), Issue 1, pg(s) 25-27

This paper attempts to provide a transparent and, if possible, a formal hierarchy of the main types of mathematical models used in the description of dynamic processes inside, at first glance, different systems. It is emphasized that the mathematical modeling is a natural and universal environment for effective analysis of system processes of different nature. From our point of view, the term "system analysis" means the methodology for classification of real systems (physical, biological, economic, social, etc.), which is based on the classification of mathematical models that are used to describe these systems.