The set of books on Mechanical Engineering and Solid Mechanics, of which this book is the first volume, is an essential tool for those looking to develop a rigorous knowledge of the discipline, whether students, professionals (in search of an approach to a problem they are dealing with), or anyone else interested.
This volume deals with the elements required for establishing the equations of motion when dealing with solid bodies. Chapter 1 focuses on the systems of reference used to locate solid bodies relative to the observer, and demonstrates how to describe their position, orientation, and evolution during their motion. Chapter 2 introduces descriptors of motion such as velocity and acceleration, and develops the concept of torsor notation in relation to these descriptors. Finally, Chapter 3 concerns the notions of mass and inertia, as well as the kinetic torsor and dynamic torsor which consolidate the kinematic and kinetic aspects in a single concept.
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) in the system of reference ‹λ› from which it is observed;
– and the forces that act upon it.
But the motion of a physical system in space is a very relative notion, which depends in an essential manner on the observer. Before any development concerning the physical system, it is, therefore, fundamental to locate it relative to its observer. This is the focus of the present chapter, in which two considerations will be examined, namely how to represent it in order to locate it, and then how to determine its location.
For all that follows, the physical system considered is the solid body, which is a continuous and rigid (this latter notion will be subsequently specified) material set.
1.1. The notion of system of reference
The system of reference is used in mechanics to set a reference, based on which it is possible to locate a mechanical element (solid body or part of an elastic medium), then to observe the evolution of its location and study its motion.
At the terrestrial scale, the favored domain of mechanics is the physical space seen from a geometrical perspective, as an affine space of a three-dimensional vector space, represented by a basis consisting of three independent vectors; this representation is important because any vector in the geometrical space of terrestrial mechanics can be expressed as a linear combination of these three vectors of the basis.
The principle of the reference system of an element located in this space thus relies on two simultaneous measurements:
– that of the distance between this element and a point in space considered as fixed reference for the motion examined;
