Lindelöf construction
From Encyclopedia of Mathematics
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A geometrical construction to find conjugate points in the problem of finding a minimal surface of revolution (see Fig.).
Figure: l058950a
Lindelöf's construction remains suitable for any variational problem of the simplest type on the -plane for which the general integral of the Euler equation can be represented in the form
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The tangents to the extremals at conjugate points and
intersect at some point
on the
-axis, and the value of the variable integral along the arc
is equal to its value on the polygonal line
(see [2]). An example is the catenoid with generating curve
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References
[1] | E. Lindelöf, "Leçons de calcul des variations" , Paris (1861) |
[2] | O. Bolza, Bull. Math. Soc. , 18 : 3 (1911) pp. 107–110 |
[3] | C. Carathéodory, "Variationsrechnung und partielle Differentialgleichungen erster Ordnung" , Teubner (1956) |
Comments
References
[a1] | A.E. Bryson, Y.-C. Ho, "Applied optimal control" , Blaisdell (1969) |
How to Cite This Entry:
Lindelöf construction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_construction&oldid=32354
Lindelöf construction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_construction&oldid=32354
This article was adapted from an original article by V.V. Okhrimenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article