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- geometry - How to find the parametric equation of a cycloid . . .
"A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line " - Wikipedia 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:
- definite integrals - Whats the area of one arch of a cycloid . . .
As for the change of variable induced by the parametrisation of the cycloid, this comes from the very definition of the differential: $$\mathrm d\mkern1 5mu x=x'(t)\,\mathrm d\mkern1 5mu t $$ Share Cite
- Finding the equation for a (inverted) cycloid given two points
A cycloid can also be interpreted the equation of motion of a point in a rolling-circle You can check here if you are not convinced Or even prove it mathematically
- How can I find the formula for a cycloid with a given speed?
$\begingroup$ The exact problem is that if I have a point on the rim of a circle of radius R that is at point (0,0) at t = 0
- calculus - Surface area by the revolution of cycloid - Mathematics . . .
Surface area by the revolution of cycloid Ask Question Asked 8 years, 8 months ago
- ordinary differential equations - The curvature of a Cycloid at its . . .
The curvature of the cycloid blows up so fast that there's only finitely much total curvature Indeed, we see geometrically that between two consective cusps, the cycloid turns exactly $\pi$ (180 degrees) That is, the integral of curvature (w r t arclength, from one cusp to the next) will be exactly $\pi$ The high curvature is over just a
- Characterizations of cycloid - Mathematics Stack Exchange
The other, smaller cycloid is being generated by a related mechanism: it is the envelope of the diameter of the rolling circle! Skipping the details, it can be shown that if the larger cycloid has the parametric equation $\left(t-\sin t\quad 1-\cos t\right)^\top$ the smaller cycloid has the corresponding equation $\left(\frac{2t-\sin 2t}{2
- Cycloid (Maths HL IA) - Mathematics Stack Exchange
I have chosen to investigate the fact that cycloid is a quicker path than the straight line for my HL Maths IA I did my own experiment and was advised to only explain up to 'timing the fall' of the brachistochrone problem by my teacher
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