Mechanics is divided into different branches according to the characteristics of the bodies it deals with; thus we speak of mechanics of material points, mechanics of rigid systems, mechanics of deformable systems, fluid mechanics, etc. At the macroscopic level, the study of the motion of bodies is carried out either within the framework of classical mechanics, which includes the mechanics of G. Galileo and I. Newton, or within the framework of relativistic mechanics, when the speed of bodies can be compared to that of light and thus the approximation of classical mechanics is no longer valid (see relativity theory).

Within the framework of classical mechanics is statistics, which studies the evolution of material systems consisting of a large number of particles, such as atoms and molecules. The laws of classical mechanics are no longer valid at the atomic or subatomic level, where the study of the corresponding systems is carried out by quantum in the two equivalent formulations of the matrix and undulatory.

When studying systems consisting of a large number of particles but of subatomic size, such as conduction electrons in a metal, classical statistical mechanics is no longer applicable and the study is carried out within the framework of quantum statistics. Even within the realm of quantum mechanics, when systems of particles in motion at speeds comparable to that of light are studied, the laws of quantum mechanics must be corrected to account for relativistic effects, and one then enters the realm of relativistic quantum mechanics. In all cases, the laws of mechanics can be expressed in purely mathematical terms, ignoring the entities under study (analytical mechanics).

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