VARIETY OF THE CASES OF INTEGRABILITY IN DYNAMICS OF A SYMMETRIC 2D-, 3D- AND 4D-RIGID BODY IN A NONCONSERVATIVE FIELD

摘要

A vast number of papers are devoted to studying the complete integrability of equations of four dimensional rigid-body motion. Although in studying low-dimensional equations of motion of quite concrete (two- and three-dimensional) rigid bodies in a nonconservative force field, the author arrived at the idea of generalizing the equations to the case of a four-dimensional rigid body in an analogous nonconservative force field. As a result of such a generalization, the author obtained the variety of cases of integrability in the problem of body motion in a resisting medium that fills the four-dimensional space in the presence of a certain tracing force that allows one to reduce the order of the general system of dynamical equations of motion in a methodical way.