Introductory note to 1899a

pp. 270-279

in: Ernst Zermelo, Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Berlin, Springer, 2013

Abstract

The physical problem treated here is to find the equations of motion for a point system subject to auxiliary conditions (constraints). In his analysis, Zermelo refers to a paper of Adolph Mayer (1899), in which the latter uses Gauss's principle to obtain solutions for several cases. Mayer gives uniqueness proofs for some simple cases (two inequalities as constraints). Zermelo both generalizes Mayer's observations and gives his own proof, which he prefaces with a geometric interpretation.