# Showing papers in "Applied Mechanics Reviews in 2002"

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TL;DR: This book discusses Classical and Modern Control Optimization Optimal Control Historical Tour, Variational Calculus for Discrete-Time Systems, and more.

Abstract: INTRODUCTION Classical and Modern Control Optimization Optimal Control Historical Tour About This Book Chapter Overview Problems CALCULUS OF VARIATIONS AND OPTIMAL CONTROL Basic Concepts Optimum of a Function and a Functional The Basic Variational Problem The Second Variation Extrema of Functions with Conditions Extrema of Functionals with Conditions Variational Approach to Optimal Systems Summary of Variational Approach Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS I Problem Formulation Finite-Time Linear Quadratic Regulator Analytical Solution to the Matrix Differential Riccati Equation Infinite-Time LQR System I Infinite-Time LQR System II Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS II Linear Quadratic Tracking System: Finite-Time Case LQT System: Infinite-Time Case Fixed-End-Point Regulator System Frequency-Domain Interpretation Problems DISCRETE-TIME OPTIMAL CONTROL SYSTEMS Variational Calculus for Discrete-Time Systems Discrete-Time Optimal Control Systems Discrete-Time Linear State Regulator Systems Steady-State Regulator System Discrete-Time Linear Quadratic Tracking System Frequency-Domain Interpretation Problems PONTRYAGIN MINIMUM PRINCIPLE Constrained Systems Pontryagin Minimum Principle Dynamic Programming The Hamilton-Jacobi-Bellman Equation LQR System using H-J-B Equation CONSTRAINED OPTIMAL CONTROL SYSTEMS Constrained Optimal Control TOC of a Double Integral System Fuel-Optimal Control Systems Minimum Fuel System: LTI System Energy-Optimal Control Systems Optimal Control Systems with State Constraints Problems APPENDICES Vectors and Matrices State Space Analysis MATLAB Files REFERENCES INDEX

1,259 citations

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TL;DR: The theoretical predictions and the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures are reviewed and the computational approaches taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models are outlined.

Abstract: Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references. @DOI: 10.1115/1.1490129#

1,097 citations

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TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.

Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

833 citations

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TL;DR: In this paper, the authors describe the interaction between oscillations and waves, and describe the absorption of wave energy by oscillating bodies by wave-energy absorption by oscillated bodies, as well as wave interactions with oscillating water columns.

Abstract: 1. Introduction 2. Mathematical description of oscillations 3. Interaction between oscillations and waves 4. Gravity waves on water 5. Wave-body interactions 6. Wave-energy absorption by oscillating bodies 7. Wave interactions with oscillating water columns Bibliography Index.

743 citations

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TL;DR: In this paper, the authors present a simulation of the transition and free-molecular regime of pressure-driven liquid flow in a shear-driven and separated liquid flow model.

Abstract: Basic Concepts and Technologies * Governing Equations and Slip Models * Shear-Driven and Separated Micro Flows * Pressure-Driven Micro Flows: Slip Flow Regime * Pressure-Driven Flows: Transition and Free- Molecular Regimes * Thermal Effects in Micro Scales * Prototype Applications of Gas Micro Flows * Electrokinetically-Driven Liquid Micro Flows * Numerical Methods for Continuous Simulation * Numerical Methods for Atomistic Simulation

612 citations

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TL;DR: In this paper, the theoretical and experimental analyses of the velocity fields with vorticity are applied to explain the physical phenomena of flow patterns of various types of vortex flows and of the flow structures in the boundary layer with high velocity gradient on a solid surface.

Abstract: In this book, the theoretical and experimental analyses of the velocity fields with vorticity are applied to explain the physical phenomena of flow patterns of various types of vortex flows and of the flow structures in the boundary layer with high velocity gradient on a solid surface. Further, the vortex flow in nature is not always circular, but also elliptic rotational flows occur under stable and unstable conditions. Therefore, the fundamental mathematical and applied descriptions of vorticity...

606 citations

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585 citations

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TL;DR: In this article, the potential of lattice models for micromechanics applications is discussed, and a detailed presentation of one-dimensional and planar lattice model for classical continua is given.

Abstract: This review presents the potential that lattice ~or spring network! models hold for micromechanics applications. The models have their origin in the atomistic representations of matter on one hand, and in the truss-type systems in engineering on the other. The paper evolves by first giving a rather detailed presentation of one-dimensional and planar lattice models for classical continua. This is followed by a section on applications in mechanics of composites and key computational aspects. We then return to planar lattice models made of beams, which are a discrete counterpart of non-classical continua. The final two sections of the paper are devoted to issues of connectivity and rigidity of networks, and lattices of disordered ~rather than periodic! topology. Spring network models offer an attractive alternative to finite element analyses of planar systems ranging from metals, composites, ceramics and polymers to functionally graded and granular materials, whereby a fiber network model of paper is treated in considerable detail. This review article contains 81 references. @DOI: 10.1115/1.1432990#

449 citations

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TL;DR: It is clear that multi-scale effects can dominate performance of friction contacts, and as a result more research is needed into computational tools and approaches capable of resolving the diverse length scales present in many practical problems.

Abstract: Friction is a very complicated phenomenon arising at the contact of surfaces. Experiments indicate a functional dependence upon a large variety of parameters, including sliding speed, acceleration, critical sliding distance, temperature, normal load, humidity, surface preparation, and, of course, material combination. In many engineering applications, the success of models in predicting experimental results remains strongly sensitive to the friction model. Furthermore, a broad cross section of engineering and science disciplines have developed interesting ways of representing friction, with models originating from the fundamental mechanics areas, the system dynamics and controls fields, as well as many others. A fundamental unresolved question in system simulation remains: what is the most appropriate way to include friction in an analytical or numerical model, and what are the implications of friction model choice? This review article draws upon the vast body of literature from many diverse engineering fields and critically examines the use of various friction models under different circumstances. Special focus is given to specific topics: lumped-parameter system models !usually of low order"—use of various types of parameter dependence of friction; continuum system models—continuous interface models and their discretization; self-excited system response—steady-sliding stability, stick/slip, and friction model requirements; and forced system response—stick/slip, partial slip, and friction model requirements. The conclusion from this broad survey is that the system model and friction model are fundamentally coupled, and they cannot be chosen independently. Furthermore, the usefulness of friction model and the success of the system dynamic model rely strongly on each other. Across disciplines, it is clear that multi-scale effects can dominate performance of friction contacts, and as a result more research is needed into computational tools and approaches capable of resolving the diverse length scales present in many practical problems. There are 196 references cited in this review-article. #DOI: 10.1115/1.1501080$

395 citations

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TL;DR: A survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material etc) under complex stress was presented in this paper.

Abstract: It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

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TL;DR: In this paper, the authors address the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays, focusing on spatial coherency and its interpretation.

Abstract: This study addresses the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays. It concentrates on the stochastic description of the spatial variation, and focuses on spatial coherency. The estimation of coherency from recorded data and its interpretation are presented. Some empirical and semi-empirical coherency models are described, and their validity and limitations in terms of physical causes discussed. An alternative approach that views the spatial variation of seismic motions as deviations in amplitudes and phases of the recorded data around a coherent approximation of the seismic motions is described. Simulation techniques for the generation of artificial spatially variable seismic ground motions are also presented and compared. The effect of coherency on the seismic response of extended structures is highlighted. This review article includes 133 references. @DOI: 10.1115/1.1458013#

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TL;DR: Mathematical Control Theory of Coupled PDEs as discussed by the authors is based on a series of lectures that are outgrowths of recent research in the area of control theory for systems governed by coupled PDE.

Abstract: Mathematical Control Theory of Coupled PDEs is based on a series of lectures that are outgrowths of recent research in the area of control theory for systems governed by coupled PDEs. The book develops new mathematical tools amenable to a rigorous analysis of related control problems and the construction of viable control algorithms. Emphasis is placed on the key role played by two interweaving features of the respective dynamical components: (1)propagaton of signularities and exceptional "sharp" regularity of the traces of the solutions of the hyperbolic component of the structure, and (2) analyticity of the solutions to the parabolic component of the structure, its propagation, and related analytic semigroup (singular) estimates.

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TL;DR: In this article, the main techniques, mathematical tools, and existing algorithms for numerical simulation of finite dimensional nonsmooth multibody mechanical systems are reviewed. And the rigid body dynamical case is examined here.

Abstract: This review article focuses on the problems related to numerical simulation of finite dimensional nonsmooth multibody mechanical systems. The rigid body dynamical case is examined here. This class of systems involves complementarity conditions and impact phenomena, which make its study and numerical analysis a difficult problem that cannot be solved by relying on known Ordinary Differential Equation (ODE) or Differential Algebraic Equation (DAE) integrators only. The main techniques, mathematical tools, and existing algorithms are reviewed.

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TL;DR: The early era The classical era The modern era Current state of porous media theory Outlook as discussed by the authors The early era, the classical era, and the modern era of media theory, see Section 2.

Abstract: Introduction The early era The classical era The modern era Current state of porous media theory Outlook.

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TL;DR: In this article, the authors showed that the linear parallel stability theory predicts the distributions of amplitudes, wave numbers, growth rates and neutral stability of the two-dimensional Tollmien-Schlichting waves.

Abstract: In experiments by Klingmann, Boiko, Westin, Kozlov and Alfredsson (1993) it became possible to remove the suction peak near the leading edge and to reduce the pressure gradient region. The experimental theoretical neutral disturbance data are given in Fig. 1. As seen, for the low frequencies, the difference between the theoretical curves appeared to be practically negligible. The experiments showed also that the linear parallel stability theory predicts well the distributions of amplitudes, wave numbers, growth rates and neutral stability of the two-dimensional Tollmien–Schlichting waves. The assumption of the boundary layer parallelity allows to acquire quite precise results for the disturbance growth rates, except for the most upper part of the neutral stability curve, where it is necessary to take into account the effects of flow nonparallelity which are quite small. The classical analysis of the linear stability treats the disturbances as separate modes of the Orr–Sommerfeld and Squire equations with exponential growth rates. However, the approach does not take into account the fact that these equations are not self-adjoint, i.e. the modes are not orthogonal. The phenomenon of the ‘lift-up’ effect (a redistribution of the streamwise momentum by small velocity perturbations in the direction normal to

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TL;DR: In this paper, butadiene polymers containing 70% or more of 1,2-structure and a relatively low melting point are produced by polymerizing 1,3-butadiene in the presence of a catalyst which has been prepared by admixing (a) an organic solvent solution containing 1, 3-Butadiene, a cobalt compound and an organoaluminium compound; (b) an amide compound of the formula (2, or (3): (2) or(3), wherein R1, R2 and R3 are

Abstract: Butadiene polymers containing 70% or more of 1,2-structure and a relatively low melting point are produced by polymerizing 1,3-butadiene in the presence of a catalyst which has been prepared by admixing (A) an organic solvent solution containing 1,3-butadiene, a cobalt compound and an organoaluminium compound; (B) an amide compound of the formula (2) or (3): (2) or (3) wherein R1, R2 and R3 are respectively an H atom, aliphatic hydrocarbon radical of 1 to 7 carbon atoms or aromatic hydrocarbon radical of 6 or 7 carbon atoms, R3 is H or an aliphatic hydrocarbon radical of 1 to 3 carbon atoms and n is 2 to 5, and; (C) carbon disulfide.

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TL;DR: In this paper, the authors present a generalization of the Riemann problem to the 1-dimensional Burgers equation, which is known as the one-dimensional Scalar Equation (SSE).

Abstract: 1 Problems.- 1.0 Outline.- 1.1 Some models.- 1.2 Basic problems.- 1.2.1 Probing problems.- 1.3 Some solutions.- 1.4 von Neumann paradoxes.- 1.5 End notes.- I Basics in One Dimension.- 2 One-dimensional Scalar Equations.- 2.1 The 1-D Burgers equation.- 2.2 Discontinuities and weak solutions.- 2.3 Rankine-Hugoniot relation.- 2.4 Nonuniqueness and entropy conditions.- 2.5 Some existence and uniqueness results.- 2.6 Some simple numerical schemes.- Exercises.- 3 Riemann Problems.- 3.1 The isentropic Euler system.- 3.1.1 Rarefaction waves.- 3.1.2 Discontinuous solutions.- 3.1.3 Entropy conditions.- 3.2 The adiabatic Euler system for polytropic gases.- 3.2.1 Rarefaction waves.- 3.2.2 Discontinuity.- 3.2.3 The entropy condition.- 3.2.4 Solutions.- 3.3 Lax's Riemann solutions.- 3.3.1 Hyperbolicity and genuine nonlinearity.- 3.3.2 The Riemann problem.- 3.3.3 Continuous solutions.- 3.3.4 Discontinuous solutions.- 3.3.5 Lax's entropy condition.- 3.3.6 Complete solutions.- 3.4 Nonconvex equations and viscous profiles.- 3.4.1 Nonconvex scalar equations.- 3.4.2 Viscous profiles.- 3.4.3 Stable viscous profiles.- 3.5 End notes and further references.- 4 Cauchy Problems.- 4.1 Smooth solutions.- 4.1.1 A new proof of blow-up in the scalar case.- 4.1.2 Systems of two equations and Riemann invariants.- 4.1.3 Blow-up and smooth solutions in systems of two equations.- 4.1.4 Remarks.- 4.2 Wave interactions.- 4.2.1 Scalar elementary wave interactions.- 4.2.2 The isentropic Euler system.- 4.3 Glimm's scheme.- 4.3.1 Glimm's scheme.- 4.3.2 Estimates.- 4.3.3 Compactness.- 4.3.4 Consistency.- 4.3.5 An example of single shocks.- 4.3.6 An example with large data (Nishida's result).- 4.4 Generalized Riemann problems.- 4.4.1 Convex scalar equations.- 4.4.2 Nonconvex scalar equations.- 4.5 2.- 7.6.2 Inner-field equations for ? ? 2.- 7.6.3 Inner-field solutions for ? = 2.- 7.6.4 Inner-field solutions for 1 > ? > 2.- 7.6.5 The case ? = 1.- 7.7 Intermediate field solutions for u0 0 u0 = 0, ? ? 1.- 7.10.3.A ? = 2.- 7.10.3.B ? > 2.- 7.10.3.C 1 0 u0 > 0, ? = 2.- 7.10.5 ?0>0 u0 > 0, ? > 2.- 7.10.6 ?0>0 u0 > 0, 1 0 u0 > 0, ? = 1.- 7.10.8 ?0>0 u0 0 u0 2.- 7.10.10 ?0>0 u0 0 u0 < 0, ? = 1.- 7.10.12 Physical description of the solutions.- 7.11 End notes.- 7.12 Appendices.- 7.12.A Finiteness of the parameters at point (1, 0, 0).- 7.12.B Proof of Lemma 7.15.- 7.13 Exercises.- 8 Plausible Structures for 2-D Euler Systems.- 8.1 The four-wave Riemann problem.- 8.2 Planar elementary waves.- 8.3 Classification/reduction.- 8.4 Some plausible structures.- 8.5 Numerical experiments.- 8.6 Vortex sheets for the incompressible Euler system.- 9 The Pressure-Gradient Equations of the Euler Systems.- 9.1 A simple splitting example.- 9.2 The pressure-gradient system.- 9.3 A four-wave Riemann problem.- 9.4 An elliptic result.- 9.5 End notes.- 9.6 Appendix.- 10 The Convective Systems of the Euler Systems.- 10.1 Systems.- 10.2 Unbounded solutions and delta waves.- 10.3 1-D theory.- 10.4 2-D Riemann solutions.- 10.5 End notes.- 11 The Two-dimensional Burgers Equations.- 11.1 Small wedge angle asymptotics.- 11.2 Weak incident shock problem.- 11.3 Weak incident shock asymptotics.- 11.4 Core region asymptotic equations.- 11.5 Initial boundary values for the 2-D Burgers system.- 11.6 Numerical solutions.- 11.7 Theoretical approaches.- 11.7.1 Shock conditions and characteristics.- 11.7.2 Regular reflection.- 11.7.3 von Neumann paradox.- 11.7.4 Global transonic problems.- 11.7.5 Riemann problems.- 11.8 End notes.- Exercises.- III Numerical schemes.- 12 Numerical Approaches.- 12.1 Generalities.- 12.2 Upwind schemes.- 12.2.1 Intuitive schemes.- 12.2.2 Linear upwind schemes.- 12.2.3 Nonlinear upwind schemes.- Exercises.- 12.3 Lax-Friedrichs scheme.- 12.4 Godunov method.- 12.5 Approximate Riemann solver.- 12.6 Higher order methods.- 12.6.1 Lax-Wendroff scheme.- 12.6.2 Slope limiter.- 12.6.3 Flux limiter.- 12.6.4 TVD (total variation diminishing) fluxes.- 12.7 Positive schemes.- 12.7.1 Motivation.- 12.7.2 Nonnegative partition (positivity) principle.- 12.7.3 One-dimensional positive schemes.- 12.7.4 Multidimensional positive schemes.- 12.7.5 Symmetrizable positive schemes.- List of Symbols.

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TL;DR: A detailed description of how microgravity conditions are obtained in various facilities available to researchers (e.g., drop towers, low-gravity aircraft flying Keplerian trajectories, Space Shuttle, International Space Station) is provided in this paper.

Abstract: Microgravity Combustion brings together, for the first time, a large and growing literature on combustion in microgravity, as collated and described by recognized experts in the field of combustion science, who are active in the specialty of combustion science in microgravity. Surprisingly, no one has provided a detailed description of how microgravity conditions are obtained in the various facilities available to researchers (e.g. drop towers, low-gravity aircraft flying Keplerian trajectories, Space Shuttle, International Space Station). This is provided in the book. The book also stresses the importance of forces and transport phenomena often neglected (sometimes without justification) in combustion processes, because these neglected or weak forces become apparent when the masking effects of buoyancy are eliminated. These forces are generally poorly taught or described in the previous literature. Examples include thermal radiative heat transfer from small flames, thermophoresis, thermocapillary flows, and purely diffusive transport. It also answers long-held questions about flammability in spacecraft. It was once thought that there would be no flammability limits in microgravity, but such limits are in fact observed and now predicted experimentally.

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TL;DR: In this article, Kane's Equations Lagrange's Equation The Triple-Rod and N-Rod Pendulum The NRod pendulum Inertia (Passive) Equation 2.1.

Abstract: INTRODUCTION REVIEW OF VECTOR ALGEBRA Equality of Vectors, Fixed and Free Vectors Vector Addition Vector Components Angle Between Two Vectors Vector Multiplication: Scalar Product Vector Multiplication: Vector Product Vector Multiplication: Triple Products Use of the Index Summation Convention Review of Matrix Procedures Reference Frames and Unit Vector Sets KINEMATICS OF A PARTICLE Vector Differentiation Position, Velocity, and Acceleration Relative Velocity and Relative Acceleration Differentiation of Rotating Unit Vectors Geometric Interpretation of Acceleration Motion on a Circle Motion in a Plane KINEMATICS OF A RIGID BODY Orientation of Rigid Bodies Configuration Graphs Simple Angular Velocity and Simple Angular Acceleration General Angular Velocity Differentiation in Different Reference Frames Addition Theorem for angular Velocity Angular Acceleration Relative Velocity and Relative Acceleration of Two Points on a Rigid Body Points Moving on a Rigid Body Rolling Bodies The Rolling Disk and Rolling Wheel A Conical Thrust Bearing PLANAR MOTION OF RIGID BODIES - METHODS OF ANALYSIS Coordinates, Constraints, Degrees of Freedom Planar Motion of a Rigid Body Instant Center, Points of Zero Velocity Illustrative Example: A Four-Bar Linkage Chains of Bodies Instant Center, Analytical Considerations Instant Center of Zero Acceleration FORCES AND FORCE SYSTEMS Forces and Moments Systems of Forces Zero Force Systems and Couples Equivalent Force Systems Wrenches Physical Forces: Applied (Active) Forces Mass Center Physical Forces: Inertia (Passive) Forces Each chapter also contains an Introduction INERTIA, SECOND MOMENT VECTORS, MOMENTS AND PRODUCTS OF INERTIA, INERTIA DYADICS Second Moment Vectors Moments and Products of Inertia Inertia Dyadics Transformation Rules Parallel Axis theorems Principal Axes, Principal Moments of Inertia: Concepts, Example, and Discussion Maximum and Minimum Moments and Products of Inertia Inertia Ellipsoid Application: Inertia Torques PRINCIPLES OF DYNAMICS: NEWTON'S LAWS AND D'ALEMBERT'S PRINCIPLE Principles of Dynamics D'Alembert's Principle The Simple Pendulum A Smooth Particle Moving Inside a Vertical Rotating Tube Inertia Forces on a Rigid Body Projectile Motion A Rotating Circular Disk The Rod Pendulum Double-Rod Pendulum The Triple-Rod and N-Rod Pendulums A Rotating Pinned Rod The Rolling Circular Disk PRINCIPLES OF IMPULSE AND MOMENTUM Impulse Linear Momentum Angular Momentum Principle of Linear Impulse and Momentum Principle of Angular Impulse and Momentum Conservation of Momentum Principles Examples Additional Examples: Conservation of Momentum Impact: Coefficient of Restitution Oblique Impact Seizure of a Spinning, Diagonally Supported Square Plate INTRODUCTION TO ENERGY METHODS Work Work Done by a Couple Power Kinetic Energy Work-Energy Principles ]Elementary Examples: A Falling Object, The Simple Pendulum, A Mass-Spring System Sk9idding Vehicle Speeds: Accident Reconstruction Analysis A Wheel rolling over a Step The Spinning Diagonally Supported Square Plate GENERALIZED DYNAMICS: KINEMATICS AND KINETICS Coordinates, Constraints, and Degrees of Freedom Holonomic and Nonholonomic Constraints Vector Function, Partial Velocity, and Partial Angular Velocity Generalized Forces: Applied (Active) Forces Generalized Forces: Gravity and Spring Forces Example: Spring-Supported Particles in a Rotating Tube Forces that do not Contribute to the Generalized Forces Generalized Forces: Inertia (Passive) Forces Examples Potential Energy Use of Kinetic Energy to obtain Generalized Inertia Forces GENERALIZED DYNAMICS: KANE'S EQUATIONS AND LAGRANGE'S EQUATIONS Kane's Equations Lagrange's Equations The Triple-Rod Pendulum The N-Rod Pendulum INTRODUCTION TO VIBRATIONS Solutions of Second-Order Differential Equations The Undamped Linear Oscillator Forced Vibration of an Undamped Oscillator Damped Linear Oscillator Forced Vibration of a Damped Linear Oscillator Systems with Several Degrees of Freedom Analysis and Discussion of Three-Particle Movement: Modes of Vibration Nonlinear Vibrations The Method of Krylov and Bogoliuboff STABILITY Infinitesimal Stability A Particle Moving in a Vertical Rotating Tube A Freely Rotating Body The Rolling/Pivoting Circular Disk Pivoting Disk with a Concentrated Mass on the Rim Rim Mass in the Uppermost Position Rim Mass in the Lowermost Position Discussion: Routh-Hurwitz Criteria BALANCING Static Balancing Dynamic Balancing: A Rotating Shaft Dynamic Balancing: the General Case Application: Balancing of Reciprocating Machines Lanchester Balancing Mechanism Balancing of Multicylinder Engines Four-Stroke Cycle Engines Balancing of Four-Cylinder Engines Eight-Cylinder Engines: The Straight-Eight and the V-8 MECHANICAL COMPONENTS: CAMS A Survey of Cam Pair types Nomenclature and Terminology or Typical Rotating Radial Cams with Translating Followers Grpahical Constructions Comments on Graphical Construction of Cam Profiles Analytical Construction of Cam Profiles Dwell and Linear Rose of the Follower Use of Singularity Functions Parabolic Rise Function Sinusoidal Rise Function Cycloidal Rise Function Summary: Listing of Follower Rise Functions MECHANICAL COMPONENTS: GEARS Preliminary and Fundamental Concepts: rolling Wheels, Conjugate Action, Involute Curve Geometry Spur Gear Nomenclature Kinematics of Meshing Involute Spur Gear Teeth Kinetics of Meshing Involute Spur Gear Teeth Sliding and Rubbing between Contacting Involute Spur Gear Teeth Involute Rack Gear Drives and Gear Trains Helical, Bevel, Spiral Bevel, and Worm Gears INTRODUCTION TO MULTIBODY DYNAMICS Connection Configuration: Lower Body Arrays A Pair of Typical Adjoining Bodies: Transformation Matrices Transformation Matrix Derivatives Euler Parameters Rotation Dyadics Transformation Matrices, Angular Velocity Components, and Euler Parameters Degrees of Freedom, Coordinates, and Generalized Speeds Transformation between Absolute and Relative Coordinates Angular Velocity Angluar Acceleration Joint and Mass Center Positions Mass Center Velocities Mass Center Accelerations Kinetics: Applied Forces Kinetics: Inertia Forces Multibody Dynamics INTRODUCTION TO ROBOT DYNAMICS Geometry, Configuration, and Degrees of Freedom Transformation Matrices and Configuration Graphs Angular Velocity of Robot Links Partial Angular Velocities Transformation Matrix Derivatives Angular Acceleration of the Robot Links Joint and Mass Center Position Mass Center Velocities, Partial Velocities, and Acceleration End Effector Kinematics Kinetics: Applied Forces Kinetics: Passive Forces Dynamics: Equations of Motion Redundant Robots Constraint Equations and Constraint Forces Governing Equation Reduction and Solution: Use of Orthogonal Complement Arrays APPLICATION WITH BIOSYSTEMS, HUMAN BODY DYNAMICS Human Body Modeling A Whole-Body Model: Preliminary Considerations Kinematics: Coordinates Kinematics: Velocities and Acceleration Kinetics: Active Forces Kinetics: Muscle and Joint Forces Kinetics: Inertia Forces Dynamics: Equations of Motion Constrained Motion Solutions of the Governing Equations Discussion: Application and Future Development APPENDICES INDEX

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TL;DR: Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems with inputs and outputs and provides a treatment of these problems using state space methods, often with a geometric flavour.

Abstract: Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, $H_2$ and $H_\\infty$ control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader's understanding of the material. Often, these exercises generalize and extend the material treated in the regular text.

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TL;DR: This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations.

Abstract: This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations. The authors use basic models to illustrate the computational issues that one might encounter when applying the SEM in a laboratory or research setting, while providing an overview of applications and computational issues regarding sensitivity calculations performed by way of continuous sensitivity equation methods (CSEM). Here they focus on the construction and analysis of algorithms for computing sensitivities. For readers already acquainted with the concept of a sensitivity equation, the authors include mathematical background for a deeper understanding of their approach. Finally, the book explores the use of SEMs for applications in the area of computational fluid dynamics, demonstrating that the early examples readers encounter in the book can be observed in the context of a more realistic physical setting. Several colour figures are included.