Van der Pol Oscillator. Technical Applications

Van der Pol equations describing self-oscillations in a quasilinear one-dimensional oscillator are generalized to the case when the generating isotropic oscillator has an arbitrary number of degrees of freedom. Two-dimensional (flat) and three-dimensional (spatial) cases are specifically considered. In contrast to the classical problem, in which a given amplitude of oscillations was stabilized, in the general case 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, etc. The technical applications of the respective models are indicated.