Cycloid - Wikipedia
网页In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve.
Cycloid -- from Wolfram MathWorld
网页2024年8月22日 · The cycloid is the locus of a point on the rim of a circle of radius rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find the area by weighing pieces of metal cut into the shape of the cycloid. Torricelli, Fermat, and Descartes all found the area.
Cycloid | Parametric curve, Geometry, Calculus | Britannica
网页Cycloid, the curve generated by a point on the circumference of a circle that rolls along a straight line. If r is the radius of the circle and θ (theta) is the angular displacement of the circle, then the polar equations of the curve are x = r(θ - sin θ) and y = r(1 - cos θ).
geometry - How to find the parametric equation of a cycloid ...
网页In many calculus books I have, the cycloid, in parametric form, is used in examples to find arc length of parametric equations. This is the parametric equation for the cycloid: $$\begin{align*}x &= r(t - \sin t)\\ y &= r(1 - \cos t)\end{align*}$$
Cycloid - Encyclopedia of Mathematics
网页2023年12月6日 · A cycloid is a periodic curve: the period (basis) is $OO_1=2\pi r$. The points $O,O_k=(2k\pi r,0)$, $k=\pm1,\pm2,\ldots,$ are cusps. The points $A=(\pi r,2r)$ and $A_k=((2k+1)\pi r,2r)$ are the so-called vertices.
19.1: Introduction to Cycloids - Physics LibreTexts
网页We now allow the circle to roll counterclockwise without slipping on the line \(y = 2a\), so that the centre of the circle moves to the right. As the circle rolls on the line, the point P describes a curve, which is known as a cycloid.
Cycloid - Vocab, Definition, and Must Know Facts | Fiveable
网页A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line. It can be described using parametric equations involving trigonometric functions.
The Cycloid - Mathonline - Wikidot
网页The cycloid is a special type of parametric curve that is traced out by a point on the circumference of the circle as it rolls along a straight line. The graph a cycloid looks like: Parametric Equation for a Cycloid. First let's determine the center of the circle.
19: The Cycloid - Physics LibreTexts
网页19.6: Motion on a Cycloid, Cusps Down We imagine a particle sliding down the outside of an inverted smooth cycloidal bowl, or a bead sliding down a smooth cycloidal wire. 19.7: The Brachystochrone Property of the Cycloid; 19.8: Contracted and Extended Cycloids; 19.9: The Cycloidal Pendulum
Cycloid -- from Wolfram Library Archive
网页A circle is rolling along a straight line without slipping. The locus of a point on the circumference of the rolling circle is called cycloid. If the point is inside or outside of the rolling circle, the locus is called trochoid.
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