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
CONTENT
to analytical dynamics -- Vibration Theory -- Probability and stochastic process -- Random vibration of structures -- Elastic system with single continuous coordinate -- Linear optimal control, theory and computation
SUBJECT
Mathematics
Applied mathematics
Engineering mathematics
Calculus of variations
Vibration
Dynamical systems
Dynamics
Mechanical engineering
Mathematics
Applications of Mathematics
Appl.Mathematics/Computational Methods of Engineering
Calculus of Variations and Optimal Control; Optimization
