New case of complete integrability of dynamics equations on a tangent bundle to a *M. V. Shamolin.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 3. P. 11-14
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 111-114].

The paper presents the results of study of the motion equations for a dynamically symmetric 4D-rigid body placed in a certain non-conservative field of forces. The form of the field is taken from the dynamics of actual 2D- and 3D-rigid bodies interacting with the medium in the case when the system contains a non-conservative pair of forces forcing the center of mass of a body to move rectilinearly and uniformly. A new case of integrability is obtained for dynamic equations of body motion in a resisting medium filling a four-dimensional space under presence of a tracking force.

*Key words*:
4D-rigid body, dynamic equations, integrability in terms of transcendental functions.