cycloid

Definitions

  • WordNet 3.6
    • adj cycloid resembling a circle
    • n cycloid a line generated by a point on a circle rolling along a straight line
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Webster's Revised Unabridged Dictionary
    • n Cycloid (Geom) A curve generated by a point in the plane of a circle when the circle is rolled along a straight line, keeping always in the same plane.☞ The common cycloid is the curve described when the generating point (p) is on the circumference of the generating circle; the curtate cycloid, when that point lies without the circumference; the prolate or inflected cycloid, when the generating point (p) lies within that circumference.
    • a Cycloid (Zoöl) Of or pertaining to the Cycloidei.
    • n Cycloid (Zoöl) One of the Cycloidei.
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Century Dictionary and Cyclopedia
    • cycloid Resembling a circle; having a circular form.
    • cycloid Specifically In ichthyology: More or less circular, with concentric striations: applied to the scales of certain fishes. See cut under scale.
    • cycloid Having somewhat circular scales, as a fish; specifically, pertaining to the Cycloidei.
    • n cycloid A curve generated by a point in the circumference or on a radius of a circle when the circle is rolled along a straight line and kept always in the same plane. When the point is in the circumference of the generating circle the curve generated is the common cycloid; when it is within the circle the curve is a prolate cycloid; and when it is on a radius produced beyond the circle the curve is a curtate cycloid. The cycloid is of great importance in relation to the theory of wave-motion.
    • n cycloid In ichthyology, a cycloid fish; a fish with cycloid scales, or one of the Cycloidei.
    • cycloid In chem., containing a cycle or ring of atoms: used especially of the structure of organic compounds.
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Chambers's Twentieth Century Dictionary
    • Cycloid a figure like a circle: a curve made by a point in a circle, when the circle is rolled along a straight line
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Etymology

Webster's Revised Unabridged Dictionary
Cyclo-, + -oid,: cf. F. cycloïde,
Chambers's Twentieth Century Dictionary
Gr. kyklos, a circle.

Usage

In literature:

In 1644 he published a tract on the properties of the cycloid in which he suggested a solution of the problem of its quadrature.
"A History of Science, Volume 2(of 5)" by Henry Smith Williams
It is not yet known to what philosopher we owe the invention of the cycloid.
"Letters on England" by Voltaire
The cycloidal curve might have been made by a Board School child.
"The Prophet of Berkeley Square" by Robert Hichens
These are called ruling machines, medallion rulers, cycloidal and geometric lathes.
"What Philately Teaches" by John N. Luff
On a map the Canary Islands look like seven irregular fish scales, and of these Grand Canary is a cycloid scale.
"A Tramp's Notebook" by Morley Roberts
Rather it travels along a cycloid, bending back upon itself, following the movement of man.
"A Novelist on Novels" by W. L. George
The cycloid is the simplest member of the class of curves known as roulettes.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8" by Various
The curves of the teeth should be cycloidal curves, although they are generally drawn in as arcs of circles.
"An Introduction to Machine Drawing and Design" by David Allan Low
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In science:

According to classical mechanics a particle with non-zero kinetic energy wanders off to in finity along snake or cycloid-like orbits winding around c ontours of constant magnetic field [13, 46].
Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
Indeed, if spin-orbit coupling is included in the calculation (while the cycloidal modulation is neglected), a small canting of the magnetic moments is obtained .
First Principles Studies of Multiferroic Materials
It has to be pointed out that no magnetization is observed in bulk BFO, where the presence of the cycloidal modulation effectively cancels any net magnetic moment.
First Principles Studies of Multiferroic Materials
If the cycloidal modulation is suppressed, either by applying a strong magnetic field or by chemical substitution a small magnetization appears, with comparable magnitude to the computational result.
First Principles Studies of Multiferroic Materials
Below TN 2 , this order transforms into a cycloidal magnetic order in which the moments now rotate in a crystallographic plane.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
Such cycloidal ordering breaks the spatial inversion symmetry and it enables the development of the spontaneous electric polarization3.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
The increase in the magnetic frustration results in the emergence of a cycloidal magnetic ground state in TbMnO3 and DyMnO3 .
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
TbMnO3 shows a sinusoidal magnetic order of the Mn spins below TN 1 = 41 K with moments oriented along the b direction, and a cycloidal order below TN 2 = 27 K with moments rotating in the bc plane.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
Sinusoidal and cycloidal modulated magnetic structures are particular cases of incommensurate magnetic order with a propagation vector k characterized by one or two magnetic vector components respectively.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
FeVO4 .23 The sinemodulated incommensurate order is obtained by imposing B = 0, and for the cycloidal order B is orthogonal to the common direction A taken by all the atomic spins in the sine-modulated phase.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
It is, however, important to note that using powder diÿraction data, the low-temperature cycloidal solution is in fact fully degenerate with a sine-modulated order where the spins are arranged in an A + B direction, thus, a direction tilted from the b axis into the bc plane.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
No evidence was found from the data for the existence of Sm order in the cycloidal phase.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
As with other ortho-manganites with cycloidal magnetic order (see inset of Fig. 1 in Ref.8 ), the magnetic propagation vector k = (0 α 0) is along the b direction (P bnm setting).
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
Decreasing the temperature, its varying magnitude indicates the relief of the exchange frustration through a change of the competing magnetic interactions, a process that stops when the cycloidal order is stabilized.
Multiferroic properties and magnetic structure of Sm1-xYxMnO3
In contrast, the chiral term gives a contribution to Pf if the magnetic structure is a cycloid.
Polarized Neutron Scattering
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