## 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.

## 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.