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unduloid : ウィキペディア英語版
unduloid

In geometry, an unduloid, or onduloid, is a surface with constant nonzero mean curvature obtained as a surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve around the line.

Image:Unduloid.jpg|This is a computer-generated unduloid created using Maple 12.

== Formula ==

Let \operatorname(u,k) represent the normal Jacobi sine function and \operatorname(u,k) be the normal Jacobi elliptic function and let \operatorname(z,k) represent the normal elliptic integral of the first kind and \operatorname(z,k) represent the normal elliptic integral of the second kind. Let ''a'' be the length of the ellipse's major axis, and ''e'' be the eccentricity of the ellipse. Let ''k'' be a fixed value between 0 and 1 called the modulus.
Given these variables,
: \operatorname(u) = -a(1-e)( \operatorname(\operatorname(u,k),k) + \operatorname(1,k)) - a(1+e)( \operatorname( \operatorname(u,k),k) + \operatorname(1,k)) \,
: \operatorname(u) = a(1+e)\operatorname(u,k) \,
The formula for the surface of revolution that is the unduloid is then
: \operatorname(u,v) = \langle \operatorname(u), \operatorname(u) \cos(v), \operatorname(u) \sin(v)\rangle \,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「unduloid」の詳細全文を読む



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