Gimbal suspension gyro: Stability, bifurcation, and chaos
The paper deals with mechanical model of gimballed gyroscope -- balanced gimbal suspension gyro (GSG) which is installed on an immovable base. External gimbal ring is under the action of viscous friction moment and moment represented by some function of the angle between external ring plane and normal vector to internal ring plane, in steady motion these planes are orthogonal. Firstly, a stability condition of uniform rotation of GSG is carried out and analyzed by means of Lyapunov's function. Also an estimation of the attraction set is obtained. Secondly, the mechanism of stability loss, when the bifurcational parameter achieves the critical value, is described. In this case a periodic motion appears, and a condition of its orbital stability is found. The third part of the paper is the investigation of forced vibration of GSG. For unperturbed system the equation of separatrix which passes through the hyperbolic points is found. To determine the condition of intersection of separatrices for perturbed system, Melnikov's distance is calculated. Its value characterises the arising of chaotic motion in the space of system's parameters.
scientific article; zbMATH DE number 1901435