Introductory note to 1930c and 1931a

pp. 672-721

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

Abstract

The navigation problem treated in Zermelo 1930c and 1931a concerns a blimp or plane that moves with a given velocity relative to the air, travelling between two points on the earth. Because of the action of wind, the motion of the airship over land is modified. Suppose that the strength and direction of the wind are given as a function of position and time. The problem is to find the trajectory followed by the airship and the corresponding steering angle such that the airship completes its journey in the least time. Zermelo gives a mathematical formulation which leads to a "navigation formula" that essentially determines the "extremal motion". He provides sufficient conditions for the existence of an extremum. The abstract 1930c considers the two-dimensional case, the paper 1931a is an extended and corrected version which also concerns the three-dimensional case.