## Duality System in Applied Mechanics and Optimal ControlA 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. |

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### Contents

1 | |

11 | |

Chapter 2 Vibration theory | 47 |

vi | 57 |

Chapter 3 Probability and stochastic process | 135 |

Chapter 4 Random vibration of structures | 161 |