Duality System in Applied Mechanics and Optimal Control

by Wan-Xie Zhong

Overview

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.

Product Details

ISBN-13:	9781475779172
Publisher:	Springer US
Publication date:	04/23/2013
Series:	Advances in Mechanics and Mathematics , #5
Edition description:	Softcover reprint of the original 1st ed. 2004
Pages:	456
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

to analytical dynamics.- Vibration Theory.- Probability and shastic process.- Random vibration of structures.- Elastic system with single continuous coordinate.- Linear optimal control, theory and computation.

Editorial 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)

From the Publisher