A straight line may be the shortest 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 between two points, but a "Brachistochrone" curve is the path of least timepic.twitter.com/aWPoz9X6i9
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A Cycloid curve is also called a "Tautochrone" (meaning equal time) Mathematically, the Brachistochrone and the Cycloid are the same curve, but they arise from slightly different but related problems (equal time & least time) Brachistochrone ⇔ Cycloid Tautochrone ⇔ Cycloid
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We learn in high school that the "period of a pendulum is independent of its amplitude"--i.e that it's isochronus. • This isn't quite true; it's only true for *small* angles θ • In reality, a pendulum's period is only independent of its amplitude if it moves along a cycloidpic.twitter.com/d1Vh1VlJ9u
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gif credits: Brachistochrone: Robert Ferréol (Wikipedia) Tautochrone: Claudio Rocchini (Wikipedia) Pendulum : Rem088roy (Wikipedia)
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A Cycloid is the curve traced out by a point on a rolling wheelpic.twitter.com/3BgmeSPDQF
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gif credit: Cycloid rolling (last gif): IchibanPL (Wikipedia)
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Keep it up, your posts are great!
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Yep you need elliptic integrals to describe the motion. Very interesting.
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Funny you should say that. I learned in high school (or its UK 1979s equivalent) that period is independent of amplitude for small angles. And I'm pretty sure they didn't teach me something different to what they taught my classmates...
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And in addition to keeping the pendulum swing short, pendulum clocks improved accuracy by having just a little bit of cycloid curve at the pivot point.
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The initial statement is true only for a small oscillation amplitide, which is normally the case for a pendulum.
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Any example of a non-cycloid movement pendulum? I can't think of any
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