With this third volume, the series on non-deformable solids reaches its acme; this is where we introduce and enlarge on the movement equations of non-deformable solids, which was always the initial goal.

The first volume of the series served to prepare the material necessary for writing these equations, that is how best to situate a solid in space to study its motion, how to describe its kinematics, the velocity and acceleration fields that drive it, how to characterize a solid through its inertial and kinetic configurations, and determine the energy statement of its motion.

But the development of this material, to arrive at the movement equations, requires various mathematical tools which the authors thought useful to remind rather than letting research them individually. This is the point of Volume 2.

With this third volume, readers are ready to touch on the core of the matter, the fundamental principle of dynamics and its application to cases where solids are free, or considered to be linked when there are bonds restricting their motion.

Chapter 1 of the book proposes a global vision of the fundamental principle and the conditions for its use, in particular the case where the observation frame of the motion of a solid is non-Galilean. The frame from which the motion of a solid is observed is crucial as it is this environment which exerts efforts upon it, affecting its progression.

The efforts, whether they are known or unknown (the links), have on the motion energetic consequences which we will evaluate by applying the fundamental principle. Chapter 2 places the solid in its environment, identifies the efforts and characterizes the power and energetic aspects they put into play throughout the motion.

The data for the problem are therefore acquired through the two first chapters, that means the following one, Chapter 3, is then in a position to begin applying the fundamental principle by presenting and enlarging on the scalar consequences that result from it and which produce the movement equations. Chapter 3 then ends with an example which serves to look through the different forms of these scalar consequences, knowing that the one which eventually is chosen depends essentially on the problem at hand.

Chapter 4 proposes two interesting cases for the application of the fundamental principle and shows how movement equations are used in various complex problems the solutions to which can only be obtained from hypotheses and simplifications without which the problem would not be treatable. These two cases are the motion of the Earth using inertial assumptions, and Foucault’s pendulum according to the study by Michel Cazin in Sciences magazine in July 2000 where he bases himself on simplifying hypotheses to propose a credible explanation to the observed motion.

Chapter 5, which is the final chapter, plays a completely different role. Developing applications of the fundamental principle and establishing its scalar consequences require being familiar with the elements which contribute to its formulation, as they are presented in the first entry in the series. To grant readers with autonomy when using this book, a methodological formulary has been included, which recaps all essential points from Volume 1. This is the purpose of Chapter 5.

Arriving at this point, it is interesting to continue exploring certain individual cases through the ways they are used. This will be the subject of the fourth and fifth books in this series; the first among them will focus on the study of equilibrium situations for non-deformable solids and on small motions (or oscillations) that they experience around them; the final entry in the series will look at the motions of solid systems including cases of equilibrium and oscillations, with an introduction to robotics.

With this present volume and with the ones that preceded it and will follow it, the authors wished to explore the motion of non-deformable solids, and provide professional or student users with a structured mathematical approach. The lessons they have been giving at the CNAM since the 1970s has convinced them of the benefits of using such an approach and encouraged them to create this series.