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Full Description
This book focuses on an area of approximations in applied mathematics known as asymptotic analysis and perturbation theory and the relatively new and powerful technique - multiple scales theory - that rests on these theories. This new theory has been applied to a large number of diverse advanced engineering systems. Engineering analysts and designers will benefit from the simplicity of the concept and applicability of the method. This book is intended to bridge the gap between esoteric mathematical theory and practical, real world applications. The book is organized into six parts. Part I presents the basic concept, foundations, and the techniques of asymptotic analysis, perturbation theory, and multiple scales. Part II treats the important areas of linear systems by the multiple scales theory. Part III covers the basic ideas governing the dynamics of flight vehicles in the atmosphere and in space. Part IV discusses aircraft applications operating within the earth's atmosphere. Space flight applications are presented in Part V, and Part VI presents some related but separate topics in appendices.
Contents
Foreword; Preface; Part I - General Theory; Introduction; Asymptotics and Approximations; Asymptotology and Dynamics Analysis; Perturbation Theory and Nonuniformities; Multiple Time Scales; Foundations and Generalization; Part II - Systems Applications; Linear Time-Invariant Systems; Linear Time-Varying Systems; Slowly Varying Linear Systems; Examples; Stability and Parameter Sensitivity; Control of Slowly Varying Systems; Turning Points; Error Analysis; Part III - Aerospace Applications: Vehicle Mathematical Model; Rigid Body Equations of Motion; Reference Frames and Coordinate Transformations; Part IV - Atmospheric Flight; Conventional Aircraft Dynamics; Re-Entry Dynamics; Hypervelocity Flight Dynamics; Stability Analysis of Hypervelocity Aircraft; Flying Qualities Through Variable Conditions; Parameter Sensitivity of High Speed Aircraft; Transition Dynamics of VTOL Aircraft; VTOL Aircraft Control Design; Boost Control of Launch Vehicles; Aircraft Wing Rock in High Angle-of-Attack Flight; A General Theory of Aircraft Wing Rock; Part V - Space Flight; Equatorial Orbit Perturbation; Satellite Attitude Prediction; Attitude Control of Spinning Satellites; Attitude Control of Dual Spin Satellites; Geomagnetic Attitude Control Design of Satellites; Deformable Reflector Stability; Active Control of Membrane Mirrors; Nonlinear Deformable Reflector; Heliogyro Spacecraft; Future Directions; Part VI - Appendixes; Extension of the nth order Derivative Operator; Earth's Gravity Field; Gravity Gradient Torque; Linear Periodic Systems and Floquet's Solution; Elliptic Integrals and Elliptic Functions; Index.
