Gyroscopic systems are different from conventional, self-adjoint mechanical systems in gyroscopic forces, which are described by non-self-adjoint operators in their equations of motion. These forces are associated with Casiolis accelerations or mass transport and sender complex dynamics. Because of this, classical linear and nonlinear analysis for conventional systems are not applicable to gyroscopic systems. This book includes five chapters on hyrodynamics and its associated emerging areas of smart structures and nonlinear methodology, which have enjoyed a great deal of attention in the recent past and which are of considerable scientific, technological and intellectual value. The synthesis of analytical, experimental and numerical methods should make this the textbook of choice for a graduate course in gyrodynamics, or as additional resource book in a graduate course in stability of mechanical structures. Moreover, the inclusion of an up-to-date bibliography should make it a valuable text for professional reference.