Spatial motion of a pendulum in a jet flow: qualitative aspects and integrability

Abstract

The presented work is devoted to the problem of motion in a resisting medium of a rigid body whose surface of contact with the medium is only a plane part of its exterior surface. In this case, the force field is constructed from the reasons for the medium action on the body under the streamline (or separation) flow around and quasi-stationarity conditions. It turns out that studying the motion of such a class of bodies reduces to systems with energy scattering (dissipative systems) or with its pumping (the so-called anti-dissipative systems) [1, 2]. Note that similar problems were already appeared in applied aerodynamics in the studies of Central Aero-Hydrodynamic Institute named after professor N. E. Zhukovskii.