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Some NonLinear Oscillatory
Elementary Theory of the First
Refinement of the First
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a2cos admittance analytical function approximate solution approximate stationary solution arbitrary constant assumes the form avoid secular terms basic equation 6.3 characteristic equation conservative systems Consider corresponding stationary solution determined differential equation 52.1 dt2 dt electrical circuit exact solution Example expansion explicitly expression finite formula Fourier series frequency fundamental harmonic given harmonic oscillation hence higher approximations impedance inductor initial amplitude initial values introduce Kryloff and Bogoliuboff Let us apply linear element method non-linear element non-linear system obtain oscilla oscillatory systems parameter periodic function periodic solution physical Pol's equation polynomial power series Prom quantity reactive power refined first approximation relation replace resistance roots self-excitation self-induction self-oscillations series circuit small oscillations solution of 6.3 spring constant stationary amplitude stationary oscillations stationary regime steady oscillations Substituting sufficiently small Suppose t+<t terms of order tf(x tion trigonometric function unstable variable velocity Vt+4 wt+e Z(ju