Stability and Control of Dynamic Systems

Description

Mechanics is the study of matter and energy on the subatomic scale. It was came into being because classical physics could not explain certain experimental results, such as why the photoelectric effect occured only when the light shone is above a certain frequency. Quantum Mechanics and Relativity became the foundation of modern physics. Fluid dynamics offers a systematic structure that underlies these practical disciplines and that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. The solution of a fluid dynamics problem typically involves calculation of various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. One of the first things that Maxwell did with his four equations, once he had obtained them, was to look for wavelike solutions. Maxwell knew that the wave-like solutions of the equations of gas dynamics correspond to sound waves, and the wave-like solutions of the equations of fluid dynamics correspond to gravity waves in water, so he reasoned that if his equations possessed wave-like solutions then these would correspond to a completely new type of wave, which he called an electromagnetic wave. If an electric field is applied to a dielectric material, each of the molecules responds by forming a microscopic dipole—its atomic nucleus will move a tiny distance in the direction of the field, while its electrons will move a tiny distance in the opposite direction. This is called polarization of the material. Dynamical systems appear in many models across sciences and technology. They can be either discrete or continuous, finite or infinite dimensional, and deterministic or with random terms. This book is intended to serve the needs of the student and practicing engineers.