what's a catenary?

Answer 1

The parametric equations for the catenary are given by

(1)
(2)
(3)

where corresponds to the vertex and is a parameter that determines how quickly the catenary "opens up." Catenaries for values of ranging from 0.05 to 1.00 by steps of 0.05 are illustrated above.

The arc length, curvature, and tangential angle for are given by

(4)
(5)
(6)

The slope is proportional to the arc length as measured from the center of symmetry.

The Cesàro equation is

(7)


The St. Louis Arch closely approximates an inverted catenary, but it has a finite thickness and varying cross sectional area (thicker at the base; thinner at the apex). The centroid has half-length of feet at the base, height of 625.0925 feet, top cross sectional area 125.1406 square feet, and bottom cross sectional area 1262.6651 square feet.

The catenary also gives the shape of the road (roulette) over which a regular polygonal "wheel" can travel smoothly. For a regular -gon, the Cartesian equation of the corresponding catenary is

(8)

where

(9)

Answer 2

A catenary is the curve that expresses the shape a chain, rope, or bridge makes when it is hanging by between two points, and pulled on by gravity. Catenary is from the latin word for "chain".

Trying not to get too geeky, but the curve is the same shape as the hyperbolic cosine function. A link is given below just in case you wish to dig into the subject further. Note: you will probably need to know at least some Algebra 2, if not more advanced math for this stuff.

Answer 3

A catenary is a curve that is described by the function y = f(x) = cosh x.

cosh x is further defined as (e^x+e^-x)/2 .

If you hang a necklace or chain by two points at equal levels, the chain will dangle down in the shape of a catenary.

Answer 4

If you connect one end of a rope to a tall pole and the other end to another similar pole some distance away, not taut, loosely, but not loose enough so that the rope touches the ground, you will notice a slight sag at the centre of the rope due to the gravity pulling down on it.

The curve described by the path of the loosely suspended rope is called a centenary curve.

[From Latin: catena = chain]


Many catenary (suspension) bridges use this concept in their design.

It somewhat resembles a segment of a parabola or part of a sine or cosine curve.

Answer 5

The catenary problem was to find the curve assumed by a loose chain hung freely from two fixed points.

Answer 6

you could no longer isolate a variable that's used the two as a multiplication and as an exponent (that's what the cosh is). The link above refers to numerical techniques (approximations) to get the respond you like. incredibly, if the catenary passes with the aid of (0,0) and yet another ingredient, in simple terms plug interior the coordinates of the different ingredient, and attempt values of "c" till you get one as close as functional. The "objective seek for" or "Solver" constructive factors of Microsoft Excel are a efficient thank you to do this.

Answer 7

1) The curve formed by a perfectly flexible, uniformly dense, and inextensible cable suspended from its endpoints. It is identical to the graph of a hyperbolic cosine.

2) Something having the general shape of this curve.

Answer 8

The kind of curve you get by holding apart the ends of a string in a uniform gravitational field. It describes the droop of the cables which hold up suspension bridges.

Answer 9

Word derived from Latin meaning chain.
In mathematics, it assumes the same shape as that described by the hyperbolic cosine function.