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词汇 Catenary curve
分类 英语词汇 英语翻译词典
释义

Catenary curve

中文百科

悬链线 Catenary

(重定向自Catenary curve)
铁链形式的悬链线。
蜘蛛丝形成多个(近似的)悬链线。
Catenarias.

悬链线是一种常用曲线,物理上用于描绘悬在水平两点间的因均匀引力作用下的软绳的形状,因此而得名。它的公式为:

y = a\cosh \frac{x}{a}或者简单地表示为y=\frac{1}{2}(e^x+e^{-x})

其中cosh是双曲余弦函数,a 是一个由绳子本身性质和悬挂方式决定的常数,x轴为其准线。具体来说,a=\frac{T_0}{g\lambda},其中g是重力加速度,\lambda是线密度(假设绳子密度均匀),而T_0是绳子上每一点处张力的水平分量,它取决于绳子的悬挂方式;若绳子两端在同一水平面上,则下面的方程决定了T_0

\frac{L}{a}=\sinh\frac{d}{a}

其中L是绳子总长的一半,d是端点距离的一半。

英语百科

Catenary 悬链线

(重定向自Catenary curve)
A hanging chain with short links forms a catenary.
Freely-hanging electric power cables (especially those used on electrified railways) can also form a catenary.
The silk on a spider's web forming multiple elastic catenaries.
Antoni Gaudí's catenary model at Casa Milà

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.

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