Multibody Dynamics

This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book’s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete.

In this work, outstanding, recent developments in various disciplines, such as structural dynamics, multiphysic mechanics, computational mathematics, control theory, biomechanics, and computer science, are merged together in order to provide academicians and professionals with methods and tools for the virtual prototyping of complex mechanical systems. Each chapter of the work represents an important contribution to multibody dynamics, a discipline that plays a central role in the modelling, analysis, simulation and optimization of mechanical systems in a variety of fields and for a wide range of applications.

This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation.

This book addresses dynamic modelling methodology and analyses of tree-type robotic systems. Such analyses are required to visualize the motion of a system without really building it. The book contains novel treatment of the tree-type systems using concept of kinematic modules and the corresponding Decoupled Natural Orthogonal Complements (DeNOC), unified representation of the multiple-degrees-of freedom-joints, efficient recursive dynamics algorithms, and detailed dynamic analyses of several legged robots.

This textbook is an introduction to and exploration of a number of core topics in the field of applied mechanics:

Flexible Multibody Dynamics comprehensively describes the numerical modelling of flexible multibody dynamics systems in space and aircraft structures, vehicles, and mechanical systems.