Catenary, the Glossary
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 in a uniform gravitational field.[1]
Table of Contents
108 relations: Acta Eruditorum, Anagram, Anchor, Antoni Gaudí, Arc length, Architects' Journal, Barcelona, Beltrami identity, Cable ferry, Calculus of variations, Cartesian coordinate system, Casa Milà, Catenary arch, Catenoid, Cesàro equation, Cf., Chain, Chain boat, Chain fountain, Christiaan Huygens, Compression (physics), Constant of integration, Ctesiphon, Curvature, Curve, David Gregory (mathematician), Davies Gilbert, Differentiable curve, Differential equation, Elasticity (physics), Electric charge, Electric field, Electromagnetic metasurface, Envelope (mathematics), Equation, Evanescent field, Floating wind turbine, Force, Frenet–Serret formulas, Funicular curve, Galileo Galilei, Gaspard-Gustave de Coriolis, Gateway Arch, Geometry, Geometry Center, Gottfried Wilhelm Leibniz, Graph of a function, Hooke's law, Hyperbolic functions, Involute, ... Expand index (58 more) »
- Roulettes (curve)
Acta Eruditorum
Acta Eruditorum (from Latin: Acts of the Erudite) was the first scientific journal of the German-speaking lands of Europe, published from 1682 to 1782.
See Catenary and Acta Eruditorum
Anagram
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once.
Anchor
An anchor is a device, normally made of metal, used to secure a vessel to the bed of a body of water to prevent the craft from drifting due to wind or current.
Antoni Gaudí
Antoni Gaudí i Cornet (25 June 1852 – 10 June 1926) was a Catalan architect and designer from Spain, known as the greatest exponent of Catalan Modernism.
Arc length
Arc length is the distance between two points along a section of a curve.
Architects' Journal
Architects' Journal is the UK’s leading professional architecture magazine, published monthly in London by Metropolis International.
See Catenary and Architects' Journal
Barcelona
Barcelona is a city on the northeastern coast of Spain.
Beltrami identity
The Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations.
See Catenary and Beltrami identity
Cable ferry
A cable ferry (including the types chain ferry, swing ferry, floating bridge, or punt) is a ferry that is guided (and in many cases propelled) across a river or large body of water by cables connected to both shores.
Calculus of variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Catenary and calculus of variations are differential equations.
See Catenary and Calculus of variations
Cartesian coordinate system
In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. Catenary and Cartesian coordinate system are analytic geometry.
See Catenary and Cartesian coordinate system
Casa Milà
Casa Milà, popularly known as La Pedrera ("the stone quarry") in reference to its unconventional rough-hewn appearance, is a Modernista building in Barcelona, Catalonia, Spain.
Catenary arch
A catenary arch is a type of architectural arch that follows an inverted catenary curve.
See Catenary and Catenary arch
Catenoid
In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution).
Cesàro equation
In geometry, the Cesàro equation of a plane curve is an equation relating the curvature at a point of the curve to the arc length from the start of the curve to the given point.
See Catenary and Cesàro equation
Cf.
The abbreviation cf. (short for either Latin confer or conferatur, both meaning 'compare') is used in writing to refer the reader to other material to make a comparison with the topic being discussed.
See Catenary and Cf.
Chain
A chain is a serial assembly of connected pieces, called links, typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression but linear, rigid, and load-bearing in tension.
Chain boat
A chain boat,John MacGregor (1867).
Chain fountain
The chain fountain phenomenon, also known as the self-siphoning beads, Mould effect, or Newton beads is a physical phenomenon observed with a chain placed inside a jar.
See Catenary and Chain fountain
Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, (also spelled Huyghens; Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution.
See Catenary and Christiaan Huygens
Compression (physics)
In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions.
See Catenary and Compression (physics)
Constant of integration
In calculus, the constant of integration, often denoted by C (or c), is a constant term added to an antiderivative of a function f(x) to indicate that the indefinite integral of f(x) (i.e., the set of all antiderivatives of f(x)), on a connected domain, is only defined up to an additive constant.
See Catenary and Constant of integration
Ctesiphon
Ctesiphon (𐭲𐭩𐭮𐭯𐭥𐭭, Tyspwn or Tysfwn; تیسفون; Κτησιφῶν,; ܩܛܝܣܦܘܢThomas A. Carlson et al., “Ctesiphon — ܩܛܝܣܦܘܢ ” in The Syriac Gazetteer last modified July 28, 2014, http://syriaca.org/place/58.) was an ancient Mesopotamian city, located on the eastern bank of the Tigris, and about southeast of present-day Baghdad.
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
David Gregory (mathematician)
David Gregory (originally spelt Gregorie) FRS (3 June 1659 – 10 October 1708) was a Scottish mathematician and astronomer.
See Catenary and David Gregory (mathematician)
Davies Gilbert
Davies Gilbert (born Davies Giddy, 6 March 1767 – 24 December 1839) was a British engineer, author, and politician.
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Differentiable curve
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus.
See Catenary and Differentiable curve
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. Catenary and differential equation are differential equations.
See Catenary and Differential equation
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.
See Catenary and Elasticity (physics)
Electric charge
Electric charge (symbol q, sometimes Q) is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
See Catenary and Electric charge
Electric field
An electric field (sometimes called E-field) is the physical field that surrounds electrically charged particles.
See Catenary and Electric field
An electromagnetic metasurface refers to a kind of artificial sheet material with sub-wavelength thickness.
See Catenary and Electromagnetic metasurface
Envelope (mathematics)
In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope. Catenary and envelope (mathematics) are analytic geometry.
See Catenary and Envelope (mathematics)
Equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign.
Evanescent field
In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source (oscillating charges and currents).
See Catenary and Evanescent field
Floating wind turbine
A floating wind turbine is an offshore wind turbine mounted on a floating structure that allows the turbine to generate electricity in water depths where fixed-foundation turbines are not feasible.
See Catenary and Floating wind turbine
Force
A force is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces.
Frenet–Serret formulas
In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space \mathbb^, or the geometric properties of the curve itself irrespective of any motion.
See Catenary and Frenet–Serret formulas
Funicular curve
In architecture, the funicular curve (also funicular polygon, funicular shape, from the fūniculus, "of rope") is an approach used to design the compression-only structural forms (like masonry arches) using an equivalence between the rope with hanging weights and standing arch with its load.
See Catenary and Funicular curve
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei or simply Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a polymath.
See Catenary and Galileo Galilei
Gaspard-Gustave de Coriolis
Gaspard-Gustave de Coriolis (21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist.
See Catenary and Gaspard-Gustave de Coriolis
Gateway Arch
The Gateway Arch is a monument in St. Louis, Missouri, United States.
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
Geometry Center
The Geometry Center was a mathematics research and education center at the University of Minnesota.
See Catenary and Geometry Center
Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz (– 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics, such as binary arithmetic, and statistics.
See Catenary and Gottfried Wilhelm Leibniz
Graph of a function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x).
See Catenary and Graph of a function
Hooke's law
In physics, Hooke's law is an empirical law which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring.
Hyperbolic functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Catenary and hyperbolic functions are Exponentials.
See Catenary and Hyperbolic functions
Involute
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. Catenary and involute are roulettes (curve).
Jacob Bernoulli
Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was one of the many prominent mathematicians in the Swiss Bernoulli family.
See Catenary and Jacob Bernoulli
Joachim Jungius
Joachim Jungius (born Joachim Junge; 22 October 1587 – 23 September 1657) was a German mathematician, logician and philosopher of science.
See Catenary and Joachim Jungius
Johann Bernoulli
Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
See Catenary and Johann Bernoulli
Kiln
A kiln is a thermally insulated chamber, a type of oven, that produces temperatures sufficient to complete some process, such as hardening, drying, or chemical changes.
Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
See Catenary and Lagrange multiplier
Leonhard Euler
Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.
See Catenary and Leonhard Euler
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
See Catenary and Limit (mathematics)
Mathematical model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language.
See Catenary and Mathematical model
Mechanical equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.
See Catenary and Mechanical equilibrium
Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area.
See Catenary and Minimal surface
Minimal surface of revolution
In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface.
See Catenary and Minimal surface of revolution
National Historic Landmark
A National Historic Landmark (NHL) is a building, district, object, site, or structure that is officially recognized by the United States government for its outstanding historical significance.
See Catenary and National Historic Landmark
Nicolas Fuss
Nicolas Fuss (29 January 1755 – 4 January 1826), also known as Nikolai Fuss, was a Swiss mathematician, living most of his life in the Russian Empire.
Normal (geometry)
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object.
See Catenary and Normal (geometry)
Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.
See Catenary and Notices of the American Mathematical Society
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
See Catenary and Numerical analysis
Overhead line
An overhead line or overhead wire is an electrical cable that is used to transmit electrical energy to electric locomotives, electric multiple units, trolleybuses or trams.
See Catenary and Overhead line
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
Parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
See Catenary and Parametric equation
Park Güell
Park Güell (Parc Güell; Parque Güell) is a privatized park system composed of gardens and architectural elements located on Carmel Hill, in Barcelona, Catalonia, Spain.
Physics
Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.
Popular Mechanics
Popular Mechanics (often abbreviated as PM or PopMech) is a magazine of popular science and technology, featuring automotive, home, outdoor, electronics, science, do it yourself, and technology topics.
See Catenary and Popular Mechanics
Position (geometry)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.
See Catenary and Position (geometry)
Radius of curvature
In differential geometry, the radius of curvature,, is the reciprocal of the curvature.
See Catenary and Radius of curvature
Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
See Catenary and Regular polygon
Robert Hooke
Robert Hooke (18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist and architect.
Roulette (curve)
In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. Catenary and roulette (curve) are roulettes (curve).
See Catenary and Roulette (curve)
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences.
See Catenary and Royal Society
Scaling (geometry)
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions.
See Catenary and Scaling (geometry)
Separation of variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
See Catenary and Separation of variables
Sheffield Winter Garden
Sheffield Winter Garden is a large temperate glasshouse located in the city of Sheffield in South Yorkshire, England.
See Catenary and Sheffield Winter Garden
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.
See Catenary and Similarity (geometry)
Simple suspension bridge
A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge in which the deck of the bridge lies on two parallel load-bearing cables that are anchored at either end.
See Catenary and Simple suspension bridge
Speed of light
The speed of light in vacuum, commonly denoted, is a universal physical constant that is exactly equal to). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.
See Catenary and Speed of light
Spring (device)
A spring is a device consisting of an elastic but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed or extended.
See Catenary and Spring (device)
Square wheel
A square wheel is a wheel that, instead of being circular, has the shape of a square.
St Paul's Cathedral
St Paul's Cathedral is an Anglican cathedral in London, England, the seat of the Bishop of London.
See Catenary and St Paul's Cathedral
St. Louis
St.
Steel catenary riser
A steel catenary riser (SCR) is a common method of connecting a subsea pipeline to a deepwater floating or fixed oil production platform.
See Catenary and Steel catenary riser
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
Stressed ribbon bridge
A stressed ribbon bridge (also stress-ribbon bridge or catenary bridge) is a tension structure similar in many ways to a simple suspension bridge.
See Catenary and Stressed ribbon bridge
Surface area
The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies.
Surface of revolution
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).
See Catenary and Surface of revolution
Suspension bridge
A suspension bridge is a type of bridge in which the deck is hung below suspension cables on vertical suspenders.
See Catenary and Suspension bridge
Tangential angle
In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the -axis. Catenary and tangential angle are analytic geometry.
See Catenary and Tangential angle
Taq Kasra
Tāq Kasrā (translit), also transcribed as Taq-i Kisra or Taq-e Kesra (طاق کسری, romanized: tâğe kasrâ) or Ayvān-e Kesrā (translit, meaning Iwan of Khosrow) are the remains of a Sasanian-era Persian monument, dated to c. the 3rd to 6th centuries, which is sometimes called the Arch of Ctesiphon.
Tension (physics)
Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object.
See Catenary and Tension (physics)
Thomas Jefferson
Thomas Jefferson (April 13, 1743 – July 4, 1826) was an American statesman, planter, diplomat, lawyer, architect, philosopher, and Founding Father who served as the third president of the United States from 1801 to 1809.
See Catenary and Thomas Jefferson
Thomas Paine
Thomas Paine (born Thomas Pain; – In the contemporary record as noted by Conway, Paine's birth date is given as January 29, 1736–37. Common practice was to use a dash or a slash to separate the old-style year from the new-style year. In the old calendar, the new year began on March 25, not January 1.
Tractrix
In geometry, a tractrix (plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the tractor) that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed.
Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
See Catenary and Translation (geometry)
Troposkein
In physics and geometry, the troposkein (from turn label)In English language scientific literature it has been variously spelled as troposkein, troposkien, troposkin, troposkine.
Two New Sciences
The Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e dimostrazioni matematiche intorno a due nuove scienze) published in 1638 was Galileo Galilei's final book and a scientific testament covering much of his work in physics over the preceding thirty years.
See Catenary and Two New Sciences
Weight
In science and engineering, the weight of an object, is the force acting on the object due to acceleration of gravity.
Weighted catenary
A weighted catenary (also flattened catenary, was defined by William Rankine as transformed catenary and thus sometimes called Rankine curve) is a catenary curve, but of a special form.
See Catenary and Weighted catenary
Whewell equation
The Whewell equation of a plane curve is an equation that relates the tangential angle with arc length, where the tangential angle is the angle between the tangent to the curve at some point and the -axis, and the arc length is the distance along the curve from a fixed point.
See Catenary and Whewell equation
Wire rope
Steel wire rope (right hand lang lay) Wire rope is composed of as few as two solid, metal wires twisted into a helix that forms a composite rope, in a pattern known as laid rope.
YouTube
YouTube is an American online video sharing platform owned by Google.
See also
Roulettes (curve)
- Astroid
- Cardioid
- Catenary
- Centered trochoid
- Cissoid of Diocles
- Cyclogon
- Cycloid
- Cycloid gear
- Deltoid curve
- Epicycloid
- Epitrochoid
- Hypocycloid
- Hypotrochoid
- Involute
- Limaçon
- Limaçon trisectrix
- Nephroid
- Roulette (curve)
- Trochoid
- Tusi couple
References
[1] https://en.wikipedia.org/wiki/Catenary
Also known as Alysoid, Catenaries, Catenary curve, Caternary, Caternary curve, Chain curve, Chainette, Hanging chain, Inverted catenary, Rope statics, Sail curve.
, Jacob Bernoulli, Joachim Jungius, Johann Bernoulli, Kiln, Lagrange multiplier, Leonhard Euler, Limit (mathematics), Mathematical model, Mechanical equilibrium, Minimal surface, Minimal surface of revolution, National Historic Landmark, Nicolas Fuss, Normal (geometry), Notices of the American Mathematical Society, Numerical analysis, Overhead line, Parabola, Parametric equation, Park Güell, Physics, Popular Mechanics, Position (geometry), Radius of curvature, Regular polygon, Robert Hooke, Roulette (curve), Royal Society, Scaling (geometry), Separation of variables, Sheffield Winter Garden, Similarity (geometry), Simple suspension bridge, Speed of light, Spring (device), Square wheel, St Paul's Cathedral, St. Louis, Steel catenary riser, Stiffness, Stressed ribbon bridge, Surface area, Surface of revolution, Suspension bridge, Tangential angle, Taq Kasra, Tension (physics), Thomas Jefferson, Thomas Paine, Tractrix, Translation (geometry), Troposkein, Two New Sciences, Weight, Weighted catenary, Whewell equation, Wire rope, YouTube.