الفهرس 
Floquet analysis of linear dynamic RLC circuitsOnly 14 pages are availabe for public view
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Abstract
Since the differential equations are widely applied for modeling many electrical applications, we concentrate our effort in this thesis to study the main qualitative properties of solutions of linear and nonlinear ordinary differential equations such as existence, uniqueness and stability. semi-analytical techniques are applied to predict the generalized output of RLC electrical circuits with time varying coefficients. Based on the resulted solutions, the proper selections of RLC parameters resulting a steady state of motion with periodic sustained modes are captured. Harmonic balance analysis is used to predict transition curves and the stability regions. An approximate expression for the Floquet form of solution is constructed via Whittaker’s method around the transition curves. Liapunov functions are used to establish necessary and sufficient conditions for the asymptotic stability related to the equivalent circuit parameters. Comparing with experimental results from specialized practical literatures, it is found that a relative satisfactory agreement with the obtained analytical results which are resulted by the linear dynamic model. Keywords: Ordinary differential equations, Parametric generator, RLC circuit, Strained parameters, Floquet Analysis, Harmonic balance, Variational Iterational Method, Stability, Liapunov functions, Fuzzy differential equations.