Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory
- Department of Electronic and Electrical Engineering, National University of Ireland, Dublin, Belfield, Dublin 4, Ireland
Abstract. Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.