Principles of Analytical System Dynamics: (Mechanical Engineering Series)

This book describes a novel approach to analytical mechanics that uses 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 analyzing systems; it is also eminently suited for constrained nonlinear models. 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. The systems considered include mechanical, thermal, electrical, and fluid elements; only discrete systems are considered. The reader is 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 practicing engineers and applied mathematicians. The text begins with an overview of system dynamics: classification and representation of motion, constraints on motion, virtual work and variational concepts. It then turns to the Lagrangian and Hamiltonian equations of motion, expressed as differential-algebraic equations. A subsequent chapter treats the dual, or complementary equations of motion, and the book concludes with a chapter on modeling and simulation, including methods of numerical solution.

Table of Contents:
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.- 2.3. Representation of Motion.- 2.4. Constraints.- 2.5. Variational Concepts.- 2.6. Geometry of Constraint.- 3. Lagrangian DAEs of Motion.- 3.1. A Variational Form of the First Law.- 3.2. Lagrange’s Equation.- 3.3. Lagrangian DAEs.- 3.4. Underlying ODEs.- 3.5. Interpretation of Lagrange’s Equation.- 4. Hamiltonian DAEs of Motion.- 4.1. Legendre Transform.- 4.2. Hamiltonian DAEs.- 4.3. Underlying ODEs.- 4.4. Comparison of Two Formulations.- 5. Complementary DAEs of Motion.- 5.1. Fundamentals.- 5.2. Complementary Lagrangian DAEs.- 5.3. Complementary Hamiltonian DAEs.- 5.4. Comparison of Two Formulations.- 6. Modeling and Simulation.- 6.1. Analysis.- 6.2. Formulating a Model.- 6.3. Numerical Solution of DAEs.- 6.4. Automated Modeling and Simulation.- 6.5. Examples.- Afterword.- References.