The basic properties of the root trajectories, which can be used for qualitative and quantitative of the dynamics of identical two-dimensional systems, are studied for characteristic equations of the form N(p) + jaM(p)= 0 with complex coefficients. Geometric and analytic methods for constructing these root trajectories are described. The degree of the trajectory equation in ω^2 is much lower than that of the characteristic equation, so it becomes easier to analyze two-channel systems described by high-order differential equations. Illustrative constructions of root trajectories are described.
Department of Oscillation Physics