Solving the problem of moving a solid body around a fixed point in a resisting medium

G U Mamatova,A О Kabdoldina,А K Sugirbekova,R A Berkutbaeva,B Hamzina

doi:10.21595/vp.2020.21453

Abstract

In this paper, we consider the problem of motion of an axisymmetric solid around a fixed point in a resistive medium, described by nonlinear dynamic Euler equations. An analytical solution to the problem when the moments of external resistance forces are proportional to the corresponding projections of the angular velocity of the body is obtained by partial discretization of nonlinear differential equations based on the theory of generalized functions. Curves of angular velocity change are constructed and graphs of comparison of these curves with previously known exact solutions are given.

Highlights

The problem of motion of a solid body with a fixed point is one of the remarkable problems of classical mechanics. The peculiarity of this problem is that, despite the important results obtained by the largest mathematicians over the past two centuries, there is still no complete solution [1,2,3,4]. These problems are reduced to the study of a system of nonlinear differential equations and differential equations with variable coefficients, obtaining analytical solutions to which is extremely difficult and is possible in a relatively small number of cases
An analytical solution of the problem is obtained by a new method called the partial discretization method
Using the partial discretization method, it is easy to obtain an analytical solution of nonlinear differential equations or differential equations with variable coefficients

Summary

Introduction

The problem of motion of a solid body with a fixed point is one of the remarkable problems of classical mechanics The peculiarity of this problem is that, despite the important results obtained by the largest mathematicians over the past two centuries, there is still no complete solution [1,2,3,4]. Using the partial discretization method, it is easy to obtain an analytical solution of nonlinear differential equations or differential equations with variable coefficients One of these equations is the dynamic Euler equations, which describes the movement of a solid body around a fixed point in a resisting medium. Using the method of partial discretization of nonlinear differential equations based on the theory of generalized functions, an analytical solution to the problem of the movement of a solid body around a fixed point in a resisting medium is obtained, which is described by the nonlinear dynamic equations of L.

Materials and methods

Results and discussion

Conclusions

Methods