Principles of Analytical System Dynamics

ISBN-13: 9780387984056 / Angielski / Twarda / 1998 / 157 str.

Richard A. Layton

Opis

Mechanical engineering, an engineering discipline borne of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound is sues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consult ing editors on the advisory board, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, en ergetics, mechanics of materials, processing, thermal science, and tribology. Fred Leckie, our consulting editor for applied mechanics and I are pleased to present this volume in the Series: Principles of Analytical System Dy namics, by Richard A. Layton. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our read ers with topical monographs as well as graduate texts in a wide variety of fields."

Spis treści

1. Introduction.- 1.1. A Perspective on Physical Systems.- 1.2. What This Book Is About.- 1.3. Background.- 1.4. Overview of Topics.- 1.5. Comments on Notation.- 2. Fundamentals of System Dynamics.- 2.1. A Unified Set of Variables.- 2.2. Classification of Discrete Elements.- 2.2.1. Kinetic Stores.- 2.2.2. Potential Stores.- 2.2.3. Ideal Dissipators.- 2.2.4. Sources.- 2.2.5. Path-Dependent Dissipation.- 2.2.6. Basic 2-Ports.- 2.3. Representation of Motion.- 2.3.1. Variable Pairs.- 2.3.2. Configuration Space and State Space.- 2.3.3. Reduced-Order Coordinates.- 2.4. Constraints.- 2.4.1. Displacement Constraints.- 2.4.2. Flow Constraints.- 2.4.3. Degrees of Freedom.- 2.4.4. Effort Constraints.- 2.4.5. Dynamic Constraints.- 2.5. Variational Concepts.- 2.5.1. Classification of Displacements.- 2.5.2. Virtual Work.- 2.5.3. Lagrange’s Principle.- 2.5.4. Classification of Efforts.- 2.6. Geometry of Constraint.- 2.6.1. Holonomic and Nonholonomic Constraints.- 2.6.2. Effort Constraints and Dynamic Constraints.- 2.6.3. Virtual Momentum.- 3. Lagrangian DAEs of Motion.- 3.1. A Variational Form of the First Law.- 3.2. Lagrange’s Equation.- 3.2.1. Derivation.- 3.2.2. Euler—Lagrange Equation.- 3.3. Lagrangian DAEs.- 3.3.1. Lagrange Multipliers.- 3.3.2. Descriptor Form.- 3.4. Underlying ODEs.- 3.4.1. Holonomic Systems.- 3.4.2. Nonholonomic Systems.- 3.4.3. Discussion.- 3.5. Interpretation of Lagrange’s Equation.- 4. Hamiltonian DAEs of Motion.- 4.1. Legendre Transform.- 4.2. Hamiltonian DAEs.- 4.2.1. Derivation.- 4.2.2. Semiexplicit Form.- 4.3. Underlying ODEs.- 4.3.1. Holonomic Systems.- 4.3.2. Nonholonomic Systems.- 4.3.3. Canonical Form.- 4.3.4. Discussion.- 4.4. Comparison of Two Formulations.- 5. Complementary DAEs of Motion.- 5.1. Fundamentals.- 5.1.1. Representation of Motion.- 5.1.2. Constraints.- 5.1.3. Classification of Flows.- 5.1.4. Work and Energy.- 5.2. Complementary Lagrangian DAEs.- 5.2.1. Derivation.- 5.2.2. Descriptor Form.- 5.2.3. Underlying ODEs.- 5.3. Complementary Hamiltonian DAEs.- 5.3.1. Derivation.- 5.3.2. Semiexplicit Form.- 5.3.3. Underlying ODEs.- 5.4. Comparison of Two Formulations.- 6. Modeling and Simulation.- 6.1. Analysis.- 6.1.1. Schematic.- 6.1.2. Coordinate Selection.- 6.1.3. Energy.- 6.1.4. Constraints.- 6.1.5. Virtual Work.- 6.2. Formulating a Model.- 6.2.1. Function Manipulation.- 6.2.2. Parameters.- 6.2.3. Initial Conditions.- 6.3. Numerical Solution of DAEs.- 6.3.1. Numerical Methods.- 6.3.2. Differential Index.- 6.3.3. Software for DAEs.- 6.4. Automated Modeling and Simulation.- 6.5. Examples.- Afterword.- References.