"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 …

Mar 29, 2015 · 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

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.

Oct 5, 2016 · Surface area by the revolution of cycloid. Ask Question Asked 8 years, 6 months ago.

Aug 8, 2020 · $\begingroup$ 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.

Aug 7, 2015 · 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 ...

Aug 17, 2014 · 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.

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 ...

May 29, 2017 · 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.

Apr 18, 2022 · The only I can think of to get rid of it is to say that the brachistochrone curve is only a segment of the cycloid so it is ok to have different differential equations and we can get rid of $^2$. ordinary-differential-equations