Geometrical Methods of Mathematical Physics

This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category.

The aim of this book is to present methods needed for the analysis of electrical machine performances in transients and steady-state conditions by means of simulations in MATLAB-Simulink and by means of FEM. This book is devoted to students, PhD students, postgraduates of electrical engineering, researchers, and scientists dealing with the analysis, design, and optimization of electrical machine properties. The purpose is to present methods used for the analysis of transients and steady-state conditions.

The main idea of the present study is to demonstrate that the qualitative theory of diffe­ rential equations, when applied to problems in fluid-and gasdynamics, will contribute to the understanding of qualitative aspects of fluid flows, in particular those concerned with geometrical properties of flow fields such as shape and stability of its streamline patterns. It is obvious that insight into the qualitative structure of flow fields is of great importance and appears as an ultimate aim of flow research.