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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, waveguide, 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 metalanguage, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for twopoint boundary value problems are proposed, which result in the numerical solutions of computer precision.Key Features of the textUnified approach based on Hamilton duality system theory and symplectic mathematics. Gyroscopic system vibration, eigenvalue problems.Canonical transformation applied to nonlinear systems.Pseudoexcitation method for structural random vibrations.Precise integration of twopoint boundary value problems.Wave propagation along waveguides, scattering.Precise solution of Riccati differential equations.Kalman filtering.HINFINITY theory of control and filter.
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