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Zeipel–Lidov–Kozai cycles is the name given to long-term interrelated changes in the inclinations and eccentricities of the orbits of natural and artificial celestial bodies. They were discovered independently by H. von Zeipel (1910), M. Lidov (1961), and Y. Kozai (1962). Originally, the existence of Zeipel–Lidov–Kozai cycles was established for nonresonant motions of celestial bodies. Approaches to studying such secular effects in the case of resonance of orbital movements appeared much later. It turned out that, at resonance, the Zeipel–Lidov–Kozai cycles may not have the symmetry that these cycles always have in nonresonant situations within the framework of the restricted three-body problem. Moreover, results of numerical studies indicate the presence of asymmetric Zeipel–Lidov–Kozai cycles in the dynamics of a number of Kuiper belt objects moving in resonance with Neptune.

The motion of an ornithopter, a flying robot, consisting of a body and two symmetric twolink wings, is considered. The device moves in a vertical plane perpendicular to the longitudinal axis of the robot. All the links of the object form a chain through cylindrical joints with parallel axes. A mathematical model of the ornithopter is developed based on a bird’s flight analysis taking into account the aerodynamic interaction of all the links with the environment. Sequences of flight phases are considered, each of which differs in the direction of motion of the wing links. As a result of numerical simulation, diagrams of the robot’s modes of motion are constructed (ascent, hovering, and descent) and the effect of the amplitude and frequency of oscillation of the wing links, as well as their area, is determined (the same wing area was achieved by varying the length and width of the wings).