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.
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© 2013 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/978-3-540-70856-8_8
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