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trochoid

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trochoid
trochoid, n. and a. (ˈtrɒkɔɪd, ˈtrəʊkɔɪd) [ad. Gr. τροχοειδής round like a wheel, f. τροχός wheel + εἶδος form: see -oid; cf. F. trochoïde (1658 in Hatz.-Darm.).] A. n. 1. Geom. A curve traced by a point on or connected with a rolling circle; orig. = cycloid 1: now usually restricted to the curtate ... Oxford English Dictionary
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Trochoid
If the point is on the circle, the trochoid is called common (also known as a cycloid); if the point is inside the circle, the trochoid is curtate; and The word "trochoid" was coined by Gilles de Roberval. wikipedia.org
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Centered trochoid
In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. wikipedia.org
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Prove parametric equations trochoid I have to show that the parametric equations of a trochoid are: $x = r\theta - d\sin\theta$ and $y=r-d\cos\theta$ where r is radius and d is the distance between center of the cir...
hard look at picture take some fixed point anywhere on the circle and when the circle is rolled around the curve drawn by the the fixed point is the TROCHOID
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Arc length of a trochoid Wolfram MathWorld gives parametric expressions for a trochoid in terms of a parameter $\phi$: \begin{eqnarray*} x &=& a\phi - b \sin \phi\\\ y &=& a - b \cos \phi, \end{eqnarray*} but then giv...
Since this is a first time I hear about trochoids, I just computed the arc length using $$\begin{eqnarray*} x &=& a\phi - b \sin (\phi) \implies x'=a -b\cos(\phi)\\\ y &=& a - b \cos (\phi)\implies y'=b \sin (\phi) \end{eqnarray*}$$ $$L=\int \sqrt{(x')^2+(y')^2} \,d\phi=\int \sqrt{a^2+b^2-2 a b \cos...
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Zaphriphyllum
Sutherland proposed the genus Zaphriphyllum for those zaphrentids which still possess a trochoid shape and pronounced cardinal fossula and consistently wikipedia.org
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trochoidal
trochoidal, a. (trəʊˈkɔɪdəl) [f. prec. + -al1.] 1. Geom. Having the form or nature of a trochoid; pertaining or relating to trochoids: see prec. A. 1.1799 Young in Phil. Trans. XC. 137 A similar chord bent into a trochoidal curve. 1861 W. Froude Rolling of Ships (1862) 23 The wave would be more accu... Oxford English Dictionary
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Prolate trochoidal mass spectrometer
These devices are sometimes called cycloidal mass spectrometers, although the path is not a cycloid (the prolate trochoid path has loops, the cycloid has wikipedia.org
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Writing y value of Curtate Trochoid in the function of x? The parametric equations of a trochoid are $x = Rt-d\sin(t)$ $y = R-d\cos(t)$ For $d < R$, there should be only one corresponding y value for every $x$ valu...
It's impossible to write $y=y(x)$ since this requires to solve the equation$$\sin t=at+b$$analytically for constants $a,b$ which is solvable only numerically.
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Pyrgulopsis carinifera
Description Pyrgulopsis carinifera is a small snail that has a height of and a trochoid shell. wikipedia.org
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Determine max/min speeds of trochoid Find the minimum and maximum speeds of the point of a trochoid and the locations where each occurs. I know a trochoid has equations $ (x)t = at - b \sin{t} $ ; $ y(t) = a- b \cos{...
For a parametric curve, the speed is just the modulus of the tangent vector, hence if $$\gamma(t)=(at-b\sin t,a-b\cos t)$$ we have $$ \dot{\gamma}(t) = (a-b\cos t,b\sin t) $$ so $$ v^2(t) = a^2+b^2-2ab\cos t $$ and the stationary points for $v(t)$ are the ones for which $\cos t=\pm 1$: $$ \max_{t} v...
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Cyclocycloid
See also Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph External links Plane curves wikipedia.org
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trochiform
trochiform, a. Zool. (ˈtrɒkɪfɔːm) [f. trochus + -[i]form.] Having the form of a trochus or top-shell; top-shaped; = trochoid a. 2.1822 J. Parkinson Outl. Oryctol. 250 The single trochiform shell, Trochus Anglicanus of Lister. 1875 C. C. Blake Zool. 257 The shell is ear-shaped, spiral, or trochiform. Oxford English Dictionary
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عجلي
إذا كانت النقطة على الدائرة، يُطلق على النوع اسم عجلي شائع (common trochoid، يعرف أيضًا بالدويري)؛ إذا كانت النقطة داخل الدائرة، يكون العجلي متقاصرًا؛ كلمة "trochoid" صاغها جيل دي روبرفال . wikipedia.org
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Ruthvenia
Description Shell is trochoid to lentiform with compressed structure. Shell color varies from light-comeous to colorless. wikipedia.org
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