"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 …

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2015年3月29日 · 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

2022年1月28日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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.

2024年3月5日 · Here we establish that the distance PT is equal to the distance OT, which then (alongside other steps) allows us to derive the parametric equation of the cycloid. Every video or written proof I have seen on the proof for deriving the parametric curve consider this step to be "intuitive", but this does not strike to me as intuitive at all.

2014年8月17日 · My lecturer proposed a question to particular result regarding the curvature of a Cycloid (generated by circle of radius 1) at its cusps. Having left it as an open problem, I thought it'd be interesting to share it here and find a hopeful answer that I can share with him.

$\begingroup$ This is actually not a completely trivial problem, because the cycloid has cusps where both $\dot x$ and $\dot y$ are zero, and a more careful analysis is needed to determine the slope of the tangent line at these points. $\endgroup$ –

2020年8月8日 · $\begingroup$ 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.

How does one derive parametric equations for the "helical cycloid"? The physical model I had in mind was a screw ramp winding around a cylinder. Supposing that there was a car that needed to go to the top of the cylinder by driving on the ramp, and supposing that a spot is placed on one of the car's wheels, what are the equations for the locus ...