Mathematical theory of stability with applications. Lyubimov V.V.

The basic concepts and theorems of the modern theory of sustainability for systems in the first approximation, conservative systems, systems, taking into account dissipative and gyroscopic forces, systems with a small parameter, are outlined. The main attention is paid to the second method of Lyapunov and his modifications. Theoretical material in the manual is accompanied by various examples of applying the theory of stability in aviation and astronautics. Interesting dynamic phenomena are considered: beating, autocolia, flutter, external stability of resonances.

The manual is intended for university students studying in the areas of training and specialties part of the UGC: “Mathematics and Mechanics”, “Physics and Astronomy” , “Electronics, radio engineering and communication systems”, “Electro- and heat engineering”, “Physico-technical sciences and technologies”, “Mechanical engineering”, “Material technologies”, “Aviation and missile and space equipment”, and other engineering and technical areas preparation. The book will be useful to graduate students, teachers and specialists in the field of solid body dynamics and space flight mechanics.