Preface
The purpose of this book is to present a substantial collection of the most
efficient algorithms for calculating rigid-body dynamics, and to explain them
in enough detail that the reader can understand how they work, and how to
adapt them (or create new algorithms) to suit the reader’s needs. The collection
includes the following well-known algorithms: the recursive Newton-Euler algo-
rithm, the composite-rigid-body algorithm and the articulated-body algorithm.
It also includes algorithms for kinematic loops and floating bases. Each algo-
rithm is derived from first principles, and is presented both as a set of equations
and as a pseudocode program, the latter being designed for easy translation into
any suitable programming language.
This book also explains some of the mathematical techniques used to for-
mulate the equations of motion for a rigid-body system. In particular, it shows
how to express dynamics using six-dimensional (6D) vectors, and it explains the
recursive formulations that are the basis of the most efficient algorithms. Other
topics include: how to construct a computer model of a rigid-body system; ex-
ploiting sparsity in the inertia matrix; the concept of articulated-body inertia;
the sources of rounding error in dynamics calculations; and the dynamics of
physical contact and impact between rigid bodies.
Rigid-body dynamics has a tendency to become a sea of algebra. However,
this is largely the result of using 3D vectors, and it can be remedied by using a
6D vector notation instead. This book uses a notation based on spatial vectors,
in which the linear and angular aspects of rigid-body motion are combined into
a unified set of quantities and equations. The result is typically a four- to six-
fold reduction in the volume of algebra. The benefit is also felt in the computer
code: shorter, clearer programs that are easier to read, write and debug, but
are still just as efficient as code using standard 3D vectors.
This book is intended to be accessible to a wide audience, ranging from
senior undergraduates to researchers and professionals. Readers are assumed
to have some prior knowledge of rigid-body dynamics, such as might be obtained
from an introductory course on dynamics, or from reading the first few chapters
of an introductory text. However, no prior knowledge of 6D vectors is required,
as this topic is explained from the beginning in Chapter 2. This book does
also contain some advanced material, such as might be of interest to dynamics
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