A new case of integrability in the dynamics of a multidimensional solid in a nonconservative field under the assumption of linear damping

Abstract

The construction of a nonconservative force field is an important point in the dynamics of a multidimen� sional solid and is based on the results taken from the dynamics of smallsize solids in the dragforce field of the medium. It becomes possible to generalize the dynamic part of the equations to the case of the motion of a multidimensional solid in a similarly con� structed field of forces and to obtain the full list of, generally speaking, transcendental first integrals expressed through the finite combination of elemen� tary functions. The results obtained are important in the sense of the presence of a nonconservative moment in the system, while it is the potential field of forces that was used previously by other authors (see, for example, (1-3)). Moreover, when constructing the force field, an additional dependence on the angular� velocity tensor is used, the introduction of which in the system is not obvious a priori (4, 5).