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Table of contents (7 chapters)
Keywords
About this book
A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision.
Key Features of the text include:
-Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems.
-Canonical transformation applied to non-linear systems.
-Pseudo-excitation method for structural random vibrations.
-Precise integration of two-point boundary value problems.
-Wave propagation along wave-guides, scattering.
-Precise solution of Riccati differential equations.
-Kalman filtering.
-HINFINITY theory of control and filter.
Reviews
From the reviews of the first edition:
"It is one of the purposes of this book, to ease the studying of applied mechanics. … The book can be used not only in the research or teaching of applied mechanics and optimal control theory, but also as a reference book for practical engineering." (Mihail Megan, Zentralblatt MATH, Vol. 1078, 2006)
Authors and Affiliations
Bibliographic Information
Book Title: Duality System in Applied Mechanics and Optimal Control
Authors: Wan-Xie Zhong
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/b130344
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2004
Hardcover ISBN: 978-1-4020-7880-4Due: 31 May 2004
Softcover ISBN: 978-1-4757-7917-2Published: 23 April 2013
eBook ISBN: 978-1-4020-7881-1Published: 11 April 2006
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: XIII, 456
Topics: Applications of Mathematics, Mathematical and Computational Engineering, Calculus of Variations and Optimal Control; Optimization, Vibration, Dynamical Systems, Control, Mechanical Engineering