E727 in the Enestrom index. This is a translation from the Latin original
Äccuratior evolutio problematis de linea brevissima in superficie quacunque
ducenda" (1779). Given a surface \$pdx+qdy+rdz=0\$, Euler wants to develop
equations that give the geodesics on this surface. I am new to the calculus of
variations, so it is not clear to me what steps follow from results that are
previously known (like the Euler-Lagrange equation in the calculations) and
what steps follow from earlier in this paper. I would appreciate comments from
any readers who are familiar with calculus of variations.
%0 Generic
%1 citeulike:3036234
%A Euler, Leonhard
%D 2008
%K Vor1800 available-in-tex-format calculus-of-variations mathematics pre1800
%T A more accurate treatment of the problem of drawing the shortest line on a surface
%U http://arxiv.org/abs/0801.0897
%X E727 in the Enestrom index. This is a translation from the Latin original
Äccuratior evolutio problematis de linea brevissima in superficie quacunque
ducenda" (1779). Given a surface \$pdx+qdy+rdz=0\$, Euler wants to develop
equations that give the geodesics on this surface. I am new to the calculus of
variations, so it is not clear to me what steps follow from results that are
previously known (like the Euler-Lagrange equation in the calculations) and
what steps follow from earlier in this paper. I would appreciate comments from
any readers who are familiar with calculus of variations.
@misc{citeulike:3036234,
abstract = {E727 in the Enestrom index. This is a translation from the Latin original
"Accuratior evolutio problematis de linea brevissima in superficie quacunque
ducenda" (1779). Given a surface \$pdx+qdy+rdz=0\$, Euler wants to develop
equations that give the geodesics on this surface. I am new to the calculus of
variations, so it is not clear to me what steps follow from results that are
previously known (like the Euler-Lagrange equation in the calculations) and
what steps follow from earlier in this paper. I would appreciate comments from
any readers who are familiar with calculus of variations.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/2caaa0f316c83baf3d7a3157a31aed869/rwst},
citeulike-article-id = {3036234},
citeulike-linkout-0 = {http://arxiv.org/abs/0801.0897},
citeulike-linkout-1 = {http://arxiv.org/pdf/0801.0897},
description = {my bookmarks from citeulike},
eprint = {0801.0897},
interhash = {466eecc1ab2a378863ef2701764f2e41},
intrahash = {caaa0f316c83baf3d7a3157a31aed869},
keywords = {Vor1800 available-in-tex-format calculus-of-variations mathematics pre1800},
month = Jan,
posted-at = {2008-07-23 08:31:21},
priority = {2},
timestamp = {2009-08-18T18:24:06.000+0200},
title = {A more accurate treatment of the problem of drawing the shortest line on a surface},
url = {http://arxiv.org/abs/0801.0897},
year = 2008
}