Journal of Theoretical
and Applied Mechanics

19, 3, pp. 355-374, Warsaw 1981

Analiza niestandardowa w mechanice newtonowskiej punktu materialnego

Czesław Woźniak

The aim of the present paper is to apply and to investigate the non-standard analysis as the mathematical tool of Newtonian mechanics. Such approach introduces into mechanics non-Archimedean ordered fields and makes it possible to describe explicitly also infinite and infinitesimal values of the physical quantities. Generally speaking, the methods of the non-standard analysis in Newtonian mechanics of mass-point systems lead to the wider class of mathematical models of physical phenomena than that which can be obtained within the classical formulation of the discrete mechanics. For example, from the ,,non-standard'' formulation of the Newton's law of motion in discrete mechanics we can derive the fundamental ,,standard'' relations of the continuum mechanics. In this part of the paper the general introduction into the non-standard analysis as well as the fundamentals of Newtonian mechanics within non-standard analysis have been outlined. As an example of applications the new interpretation of the standard concept of constrains has been derived from the Newton's law of motion of certain non-standard unconstrained mass-point systems.