Mechanics deals with the dynamics of particles, rigid bodies, continuous media (fluid, plasma, and elastic materials), and field theories such as elec- tromagnetism and gravity. This theory plays a crucial role in quantum me- chanics, control theory, and other areas of physics, engineering, and even chemistry and biology. Clearly, mechanics is a large subject that plays a fundamental role in science. Mechanics also played a key part in the devel- opment of mathematics. Starting with the creation of calculus stimulated by Newton’s mechanics, it continues today with exciting developments in group representations, geometry, and topology; these mathematical devel- opments in turn are being applied to interesting problems in physics and engineering.
Symmetry plays an important role in mechanics, from fundamental for- mulations of basic principles to concrete applications, such as stability cri- teria for rotating structures. The theme of this book is to emphasize the role of symmetry in various aspects of mechanics.
This introduction treats a collection of topics fairly rapidly. The student should not expect to understand everything perfectly at this stage. We will return to many of the topics in subsequent chapters.