Principles of Analytical System Dynamics

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.