Abstract
Zermelo considers relative and absolute minima of geodesics, which he calls shortest and by far shortest paths, respectively. The infinitesimal variational technique first takes into account only sufficiently close comparison functions that lie in a given neighborhood of the extremal, leading to necessary conditions for relative extrema, in this case minima. Zermelo mentions three possible ways to extend the associated variational problem, which can be characterized by the following key words: (a) absolute minima, (b) restrictions on surfaces, (c) differential inequalities as constraints. The cases (b) and (c) appear naturally in practical questions, among them the problem of road and rail construction.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Thiele, R. (2013). Introductory note to 1902d. In: Ebbinghaus, HD., Kanamori, A. (eds) Ernst Zermelo - Collected Works/Gesammelte Werke II. Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70856-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-70856-8_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70855-1
Online ISBN: 978-3-540-70856-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)