This paper considers the use of harmonic linearization as applied to the analysis of nonlinear automatic control systems. This approach, which has been proven in practical engineering applications, involves the replacement of a nonlinear equation by a linear equation. In establishing the method a small parameter is considered which makes it possible to speak with some degree of approximation of the solution of the new equation to that of the given linear equation. Thus, the mathematics of nonlinear mechanics is brought to bear on the problem by explaining and extending the usefulness of automatic control theory and nonlinear systems.

The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.

Theory of Automatic Control focuses on the theory of automatic control, including controllers, models, control processes, and analysis of systems. The book first offers information on the general introduction to automatic controllers and the construction of a linear model control system and the initial material for its analysis. Discussions focus on astatic controllers of indirect action, floating feedback, controllers of discontinuous action, static characteristics of elements and of systems, and frequency characteristics of a linear element and of the linear model of a system. The text then ponders on the stability of the linear model of an automatic control system and the construction and evaluation of the processes in the linear model of a system of automatic control. Topics include construction of the process from the transfer function of the system; construction of the control process from the frequency characteristics of the system; and analysis of systems with random disturbances given statistically. The publication takes a look at auto- and forced oscillation in non-linear systems, including approximate determination of forced oscillations in the presence of an external periodic action and determination of the auto-oscillations in the case of auto-resonance. The manuscript is a dependable reference for readers interested in the theory of automatic control.

The Dynamics of Automatic Control Systems focuses on the dynamics of automatic control systems and the fundamental results of the theory of automatic control. The discussion covers theoretical methods of analysis and synthesis of automatic control systems common to systems of various physical natures and designs. Concrete examples of the simplest functional circuits are presented to illustrate the principal ideas in the construction of automatic control systems and the application of the theoretical methods. Comprised of 19 chapters, this book begins by describing different forms of automatic control systems, with emphasis on open and closed loop automatic systems. The reader is then introduced to transients in automatic regulation systems; methods for improving the regulation process; and some problems in the theory of automatic regulation. Subsequent chapters deal with linearization and transformation of the differential equations of an automatic regulation system; stability criteria for ordinary linear systems; equations of systems with delay and with distributed parameters; and equations of nonlinear automatic regulation systems. The oscillations and stability of nonlinear systems are also considered. This monograph will be of interest to engineers and students.

So far, very careful investigations have been made regarding the flight properties, in particular the static and dynamic stability, of engine-propelled aircraft and of untowed gliders. In contrast, almost no investigations exist regarding the stability of airplanes towed by a towline. Thus, the following report will aim at investigating the directional stability of the towed airplane and, particularly, at determining what parameters of the flight attitude and what configuration properties affect the stability. The most important parameters of the flight attitude are the dynamic pressure, the aerodynamic coefficients of the flight attitude, and the climbing angle. Among the configuration properties, the following exert the greatest influence on the stability: the tow-cable length, the tow-cable attachment point, the ratio of the wing loadings of the towing and the towed airplanes, the moments of inertia, and the wing dihedral of the towed airplane. In addition, the size and shape of the towed airplane vertical tail, the vertical tail length, and the fuselage configuration are decisive factors in determining the yawing moment and side force due to sideslip, respectively.