The mathematical representation of a system Mécanique is important in mechanics (and in Physique in general). This representation will be more or less complex according to the level of detail of the model and the phenomenon which one seeks to model.

Definition

One calls Point material or specific Corps a mechanical system whose dimensions are small in front of the distances characteristic of the studied movement (distance covered, ray of an orbit…). The mechanical system is then modelled by a geometrical point M with which its mass m is associated.

Note::

1. generally, little attention is carried to the concept of material point in the courses of Mécanique. One often speaks about " point" without another precision, heard with the mathematical direction of the term.
2. the concept of material point is to some extent during that of specific Charge, frequently used in electromagnetism.

Discussion and examples

The model of the material point is simplest that one can consider for a mechanical system. No information on the geometrical form of the real system, the distribution of the matter (of the masses) in its center, etc is preserved. The only physical size characteristic of the system is its Masse m .

The validity of this model depends on the one hand nature on the movement as of the phenomenon which one seeks to model. The two following examples makes it possible to clarify these last points.

Examples: movements of revolution and clean rotation of the Earth.

In a Heliocentric Reference frame , it is possible to study the movement of revolution of the Earth by regarding the latter as a material point T of mass M_T = 5,98.10²⁴ kg . Indeed its ray R_T≈6400 km is much lower than the average distance Ground - Sun D ≈ 1,5.10⁸ km , or than the Périmètre of the orbit (approximately 9.10⁸ km). It is thus possible to regard the very whole Earth as reduced to a point.

On the other hand for the study of the own rotation movement of the Earth, in the Référentiel Géocentrique, it is obvious that one could not regard the latter as a simple material point. It is necessary to take account of its form and the distribution of the masses in its center: the model simplest, well-known, and that of a sphere of ray R_T and center T , homogeneous or at least with spherical distribution of mass.

See too

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