LAGRANGE OR EULER? PART TWO: THE PRESENT

Abstract

This paper represents the second put of a series of articles on the EULERIAN and Lagrangean dynamical traditions, the first part [1] of which was published in this Annual. The present state of affairs in analytical mechanics may be characterised as an eclectic coexistence of two opposite tendencies — the Eulerian and the Lagrange dynamical traditions. The most typical features of both are analised in this article and corresponding conclusions are drawn. According to them, no alternative of the Eulerian dynamical axioms (the laws or principles of momentum and of kinetical moment of rigid' bodies) is possible, the Lagrangean dynamical equations being only their projections on appropriate axes.). This paper is a preliminary preparation for the solution of Hilbert's sixth problem concerning the axiomatical consolidation of the logical foundations of analytical mechanics.