Principles of Analytical System Dynamics

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.