The Van der Pol Spatial Oscillator. Technical Applications in Modern Gyroscopy

The modified Van der Pol equations describing self-oscillations in a quasi-linear one-dimensional oscillator are generalized to the case when the generating oscillator has an arbitrary number of degrees of freedom. One-dimensional, two-dimensional (flat), and three-dimensional (spatial) cases are considered specifically. In contrast to the classical problem, in which a given oscillation amplitude has stabilized, in general, it is possible to stabilize not only the oscillation energy, but also the area of a flat elliptical trajectory, its orientation in space, the frequency of the oscillatory process, precession, etc. The types of oscillator are studied: classical, with one degree of freedom, performing rectilinear oscillations, two-dimensional, performing plane oscillations, and three-dimensional (spatial). The purpose of the work is to study the possibilities of creating spatial wave solid-state gyros (WSG) of integrating type.