MECHANICS. - Mechanics has as its objective the study of the phenomena of material bodies that occur without altering either their physical or chemical nature. It will therefore study, for example, the flow of water in channels or pipes, the transfer of its kinetic energy to devices capable of absorbing and utilizing it, and any other phenomenon that leaves the nature of water unchanged. It will not, however, concern itself with the possible evaporation or transformation of water into water vapor, nor much less with its possible decomposition into its constituent elements, oxygen and hydrogen. Already from ancient times it had been recognized that in mechanical phenomena relationships between quantities inherent in motion, forces, and some intrinsic property of the material bodies involved are at play. It is therefore useful, before fully addressing the problem of determining those relationships, to undertake a preliminary general study both of motion (kinematics or geometry of motion) and of forces.
I. KINEMATICS
Observation teaches that every displacement is always accompanied by an act of motion that unfolds in space with a certain continuity and in close correlation with time, or, as is often said, as a function of time.The study of possible acts of motion is the primary aim of kinematics, which thereby justifies its designation as the geometry of motion. As is intuitive, to follow and possibly to express formally acts of motion, one must resort to some system of reference, which, however, can generally be chosen with considerable arbitrariness. But already at this point a fundamental difference between kinematics and geometry becomes apparent. The latter always selects the system of reference it intends to adopt from among infinite systems assumed to be at relative rest, that is, fixed with respect to one another, even when this is not explicitly stated. For example, the position of a point in a room can be simply referred to a system of Cartesian coordinates whose axes are formed by three edges of the walls converging at one of the corners, or to any system of polar coordinates with its pole at that corner. In any case, the position of the point is always understood relative to the chosen system of reference. Now, if it is supposed that the point is in a certain motion with respect to the chosen system of reference, it will be in motion equally with respect to all the others. In the case now considered, motion would therefore have an absolute character. But, once the notion of motion is introduced, it is logical to apply it also to systems of reference and thus to consider systems of reference in relative motion with respect to one another. In such a case, however, the notion of the motion of a body loses any absolute meaning and remains a notion relative to the chosen system of reference, which will always need to be indicated unless it can be implicitly understood without ambiguity.
Among all the systems in relative motion that are possible