http://worldcat.org/entity/work/id/13487025

Duality system in applied mechanics and optimal control

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.

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