Mechanics of the discrete and continuous systems in the light of the non-standard analysis
Abstract
Within the known treatment of Newtonian Mechanics, i.e., when the classical analysis is the mathematical tool of mechanics, the real bodies are represented either by the mass-point discrete systems or by the material continua. Thus the discrete mechanics and the continuum mechanics constitute two separate branches within classical formulation of Newtonian mechanics. In the contribution we are to show that if the foundations of mechanics are expressed in terms of the non-standard analysis then the real bodies can be represented exclusively by the mass-point systems and we can confine ourselves to the discrete (but "non-standard") mechanics only. All classical material systems (including material continuum) can be obtained by introducing different topologies to the non-standard metric space in which the fixed non-standard mass-point system is embeded. The reader is assumed to be familiar with the basic concepts of the non-standard analysis given in [1-4].
Domains
Mechanics [physics.med-ph]
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