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.
-HINFINITY theory of control and filter.
- Book Title Duality System in Applied Mechanics and Optimal Control
- Series Title Advances in Mechanics and Mathematics
- DOI https://doi.org/10.1007/b130344
- Copyright Information Kluwer Academic Publishers 2004
- Publisher Name Springer, Boston, MA
- eBook Packages Springer Book Archive
- Hardcover ISBN 978-1-4020-7880-4
- Softcover ISBN 978-1-4757-7917-2
- eBook ISBN 978-1-4020-7881-1
- Edition Number 1
- Number of Pages XIII, 456
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Applications of Mathematics
Mathematical and Computational Engineering
Calculus of Variations and Optimal Control; Optimization
Vibration, Dynamical Systems, Control
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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)