Abstract
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.
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