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Hertz: Material Particle and Material Point

Here we will consider the concepts of material particle and material point as defined by Hertz (Hertz 2003, pp. 45 - 46). The material particle is indestructible, and can serve in the definition of a force through the Third Principle of Mechanics as we know it, while a material point is an entity composed of material particles. The congregation of particles in a material point is not the simple process that might appear at a superficial sight. Two observations must be made before starting either the synthetic construction or the analysis of a material point. First of all, one must keep in mind that the particles have to maintain their identity regardless their location. This is implied by the invariability and indestructibility of a particle. Therefore, inside a material point, the particles possess repulsion towards all the other particles of the material point. If this condition doesn’t exist, a particle cannot be invariable, but variable through adding of other particles, i.e. it would be actually a material point. Indeed, unlike the material particle a material point is variable and destructible. Especially the destructibility is sometimes described as a disintegration of a certain material point in a set of material points, although not material particles. In order to make the destructibility possible we need to introduce the physical condition of attraction between particles, for otherwise the material point could not exist; therefore the material particles in a material point possess attraction towards the other particles of the material point, but not towards all of them, otherwise the material point would not be destructible.

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