This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklos Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.'s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.

This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler's theory of the elastica, Kirchhoff 's theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.

Suitable for both senior-level and first-year graduate courses, this fully revised edition provides a unique and systematic treatment of engineering dynamics that covers Newton-Euler and Lagrangian approaches. New to this edition are: two completely revised chapters on the constraints on, and potential energies for, rigid bodies, and the dynamics of systems of particles and rigid bodies; clearer discussion on coordinate singularities and their relation to mass matrices and configuration manifolds; additional discussion of contravariant basis vectors and dual Euler basis vectors, as well as related works in robotics; improved coverage of navigation equations; inclusion of a 350-page solutions manual for instructors, available online; a fully updated reference list. Numerous structured examples, discussion of various applications, and exercises covering a wide range of topics are included throughout, and source code for exercises, and simulations of systems are available online.