Symmetry in Mechanics

"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu­ dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap­ preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe­ maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists.

"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu­ dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap­ preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning.

Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science.

This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics.

The Second International Conference “Symmetry in Nonlinear Mathematical Physics” was organized mainly due to efforts of Professor Wilhelm Fushchych. It happened, however, that this out- standing scientist and kind person passed away. The Conference was dedicated to his memory. Among 80 participants of the Conference there were representatives of 14 countries from 5 continents. The main part of the lectures was devoted to investigation of symmetries and construction of exact solutions of nonlinear differential equations.