A novel approach to analytical mechanics, using differential-algebraic equations, which, unlike the usual approach via ordinary differential equations, provides a direct connection to numerical methods and avoids the cumbersome graphical methods that are often needed in analysing systems. Using energy as a unifying concept and systems theory as a unifying theme, the book addresses the foundations of such disciplines as mechatronics, concurrent engineering, and systems integration, considering only discrete systems. Readers are expected to be familiar with the fundamentals of engineering mechanics, but no detailed knowledge of analytical mechanics, system dynamics, or variational calculus is required. The treatment is thus accessible to advanced undergraduates, and the interdisciplinary approach should be of interest not only to academic engineers and physicists, but also to practising engineers and applied mathematicians.

Inhalt

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.