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This paper presents a Newton‐Raphson algorithm for determining the Fourier spectrum of two‐periodic solutions for dynamic systems described by nonlinear ordinary differential equations. Assuming that two basic frequencies are known, the coefficients of a double Fourier series result from this algorithm. An application to the analysis of electromagnetic phenomena in electromechanical converters is described. In an example, of the steady‐state performances of current in a simple converter, the algorithm is tested with very good results.

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This paper presents an approach which transforms the problem of finding the general solutions of linear ordinary differential equation systems with periodic coefficients in eigenvalue and eigenvector problems of an infinite matrix. The problem of determining particular integrals for almost periodic input functions is also presented. This is equivalent to a problem of solving infinite linear algebraic equations. The paper includes an example application of the approach to the analysis of a simple electromechanical system. Results of numerical tests are also given.

The paper presents a new method of determining the steady-state of electrical circuits with nonlinear elements whereas periodic solution can be predicted. This method allows for calculating steady-state wave-forms directly in time domain. A new discrete differential operator has been defined. It reduces nonlinear differential equations of a circuit to a set of algebraic equations for the values of the steady state solution at discrete time instants. Based on it an algorithm for solving nonlinear differential equations has been proposed. Numerical tests have been performed for elementary electrical circuits with a nonlinear coil and a power electronic switching element.