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Difference between revisions of "Sturm curves"

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Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090740/s0907401.png" />-axis — a [[Catenary|catenary]].
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Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the $x$-axis — a [[Catenary|catenary]].
  
 
These curves were studied by J.Ch. Sturm.
 
These curves were studied by J.Ch. Sturm.

Latest revision as of 11:44, 5 July 2014

Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the $x$-axis — a catenary.

These curves were studied by J.Ch. Sturm.

References

[1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)


Comments

Replacing "rolls along a straight line" by "rolls along another fixed curve" , the point will describe a roulette.

References

[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
[a2] F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
How to Cite This Entry:
Sturm curves. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sturm_curves&oldid=32373
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article