Low-Dimensional and Multi-Dimensional Pendulums in Nonconservative Fields. Part 1

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

“…System ( 1) is a dynamic system with variable dissipation and with zero mean (with respect to the angle of attack) [3]. This means that the integral of the divergence of its right-hand side over the period of the angle of attack, which describes the variation in the phase volume (after the appropriate reduction of the system), is equal to zero.…”

“…In this case, the transcendence is meant in the complex analysis sense, i.e., after the continuation of the functions considered to the complex domain, they have essentially singular points. The latter fact is stipulated by the existence of attracting and repelling limit sets in the system considered (for example, attracting and repelling foci) [3,4].…”