In this video I go over the cycloid curve and derive the parametric equations for the case in which the angle inside the circle is between 0 and π/2. The cycloid is formed by tracing a point on the circumference of a circle as it rotates along a straight line. The resulting parametric equations are shown below:
x = r(θ - sinθ)
y = r(1 - cosθ)
Although I derived these equations for the case where θ is between 0 and π/2, these equations do in fact work for all values of θ. I will go over the proof for other values of θ in a later video so stay tuned for that!
Also, these parametric equations can be rearranged to eliminate θ and to write x as a function of y, but the resulting Cartesian equation is much more complicated. I will nonetheless derive the Cartesian form of the cycloid in a later video, as well as the very interesting history of the cycloid, so stay tuned!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht9rJUo4SMEVW-eiJg
View Video Notes on Steemit: https://steemit.com/steemstem/@mes/parametric-curves-example-7-the-cycloid-proof-part-1
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I don't always derive parametric equations but when I do they usually are for the famous Cycloid Curve ;)
View Video Notes: https://steemit.com/steemstem/@mes/parametric-curves-example-7-the-cycloid-proof-part-1
It's really informative and helpful blog about mathmetics. You have shared very useful videos about parametric curves.
Thanks for sharing this excellent work.