This monograph deals with the controlled/non-controlled nonlinear systems of differential equations. A mathematical apparatus is developed to construct stationary conditions and to carry out studies on the behaviour of integral curves in the neighbourhood of such conditions.Considerable coverage is given to existence and methods of finding periodic orbits and almost-periodic solutions, as well as to the description of the class of ergodic recurrent motions. There is further treatment of the perturbation method and the theory of time-independent and periodic perturbations in particular.The theory developed here is applied to the construction and investigation of the neigbourhood of time-independent conditions for nonlinear systems of automatic control, and the control of charged particle beam in magnetic field. Some other specific problems are also solved such as after effect systems and orbit quantization.
The author applies methods of nonlinear elasticity to investigate the defects in the crystal structure of solids such as dislocations and disclinations that characterize the plastic and strength properties of many materials. Contrary to the geometrically motivated nonlinear theory of dislocations continuously distributed over the body, nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book, and in a form accessible to both students and researchers. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions are found. The nonlinear approach to investigating the isolated defects produces results that often differ qualitatively from those of the linear theory.
Worked Examples in Physics: A Textbook for Private Study consists of worked examples encountered at examinations in secondary schools at Moscow University. The examples for this collection focus on those physical questions, situations, and laws that give rise to the most number of errors. Organized into two parts, this book begins with an overview of several problems that have been specially selected to show in detail the methods of applying the more important laws, which often are not mastered by the student. This text then discusses the general methods of solving problems by means of the resolution and composition of the motion. This book discusses as well a large number of examples that serves to indicate how one may reduce the solution of a complicated problem on curvilinear motion to the solution of a simple and previously solved problem dealing with two independent linear motions. This book is a valuable resource for secondary school students.
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