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An Incidental Role of the Material Particle

The second point of Hertz’s definitions, which is the most important for us, regards the material particles. A material particle to Hertz endows a point in space not only with identity, a task for which the definition is mainly intended, but with an indestructible material ‘anchor’ so to speak. It is not too hard to see that, besides being indicator for a point in space, such a material particle is, incidentally, the most convenient point of application of a force, and can thus sustain also the Third Principle of Dynamics, inasmuch as it is conceived as “invariable and indestructible”.

     Let’s recall once again that, in modeling the reality around us we have exclusively only the possibility to deal with material points in the acceptance of Hertz. This is the most we can say about the mathematical object we work with. Indeed, we are perfectly conscious that a star, for instance, is actually an extended body, and only due to the distance we see it as a point. Therefore we have to accept that a material point is itself a complicated structure, and this fact is duly noted in Hertz’s formalism: the material points are made of material particles! Come to think of it: this very definition liberates us from the necessities of removing the forces from the stage. Indeed, a material particle can support an acting force on it, and this acting force is present with its defining reacting force. In a word, in the structure of a material point, a material particle is as free as it can be, given the environment. As a matter of fact, this was entirely Newton’s philosophy!

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