LAGRANGE OR EULER? PARTH THREE: THE FUTURE

Abstract

This paper is the third part of a series of articles on the Eulerian and Lagrangean dynamical traditions, the first two parts [1,2] of which have been published in this Annual. It contains some conceptions on the future development of the investigations on the stabilization of the logical foundations of analytical mechanics, as the authors see it; in this connection Hilbert's sixth problern on the axiomatic consolidation of these foundations is, naturally,inevitable. After an analysis of the present state of affairs concerning the bask mechanical entities, as for instance the geometrical background of analytical mechanics, the theory of arrows as the genuine mathematical interpretation of the force Concept, the motions in standard vector spaces, the rigid body concept, etc., corresponding definitions are proposed together with the main corollaries they imply. The article makes on a large scale use of results obtained in previous publications of the authors.