Probabilistic models for dynamical systems

Content: Introduction     Applications    Units    Organization of the Text    Quotes    Problems    Events and Probability     Sets    Probability     Summary    Quotes    Problems    Random Variable Models     Probability Distribution Function    Probability Density Function    Probability Mass Function    Mathematical Expectation    Mean Value    Useful Continuous Probability Density Functions    Discrete Density Functions    Moment-Generating Function    Two Random Variables    Summary    Quotes    Problems    Functions of Random Variables     Exact Functions of One Variable    Functions of Two or More Random Variables    Approximate Analysis    Monte Carlo Methods    Summary    Quotes    Problems    Random Processes     Basic Random Process Descriptors    Ensemble Averaging    Stationarity    Correlations of Derivatives    Fourier Series and Fourier Transforms    Harmonic Processes    Power Spectra    Narrow- and Broad-Band Processes    Interpretations of Correlations and Spectra    Spectrum of Derivative    Fourier Representation of a Stationary Process    Summary    Quotes    Problems    Single Degree-of-Freedom Vibration     Motivating Examples    Newton's Second Law    Free Vibration With No Damping    Harmonic Forced Vibration With No Damping    Free Vibration with Viscous Damping    Forced Harmonic Vibration    Impulse Excitation    Arbitrary Loading    Frequency Response Function    SDOF: The Response to Random Loads    Response to Two Random Loads    Summary    Quotes    Problems    Multi Degree-of-Freedom Vibration     Deterministic Vibration    Response to Random Loads    Periodic Structures    Inverse Vibration    Random Eigenvalues    Summary    Quotes    Problems    Continuous System Vibration     Deterministic Continuous Systems    The Eigenvalue Problem    Deterministic Vibration    Random Vibration of Continuous Systems    Beams with Complex Loading    Summary    Quotes    Problems    Reliability     Introduction    First Excursion Failure    Other Failure Laws    Fatigue Life Prediction    Summary    Quotes    Problems    Nonlinear and Stochastic Dynamic Models     The Phase Plane    Statistical Equivalent Linearization    Perturbation Methods    The Mathieu Equation    The van der Pol Equation    Markov Process-Based Models    Summary    Quotes    Problems    Non-stationary Models     Envelope Function Model    Non-stationary Generalizations    Priestley's Model    Oscillator Response    Multi Degree-of-Freedom Oscillator Response    Nonstationary and Nonlinear Oscillator    Summary    Quotes    Problems    Monte Carlo Methods     Introduction    Random Number Generation    Joint Random Numbers    Error Estimates    Applications    Summary    Quotes    Problems    Fluid-Induced Vibration     Ocean Currents and Waves    Fluid Forces in General    Examples    Available Numerical Codes    Summary    Quotes    Probabilistic Models in Controls and Mechatronic Systems     Concepts of Deterministic Systems    Concepts of Stochastic Systems    Filtering of Random Signals    White Noise Filters    Stochastic System Models    The Kalman Filter    Additional Issues    Summary    Quotes    Index