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 one for which all objects take the 𝑠𝑎𝑚𝑒 amount of time to reach the bottom • If this seems counterintuitive, remember that 𝑚𝑔ℎ=½𝑚𝑣², and so objects starting higher will have a larger final velocitypic.twitter.com/EV4ZzT6YFo
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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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Tautochrone reminded me of tautology. Do they share anything?
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Just the Greek roots! Tautology =same logic, Tautochrone=same time
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Gotcha
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For some reason, we don't touch on this enough (or at all) when teaching PHYS-I for engineering majors (or even science majors), and then, when we get to Classical Mechanics for physics majors later on, this is kind of "easy" and it again doesn't receive a proper attention
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On the model of your profile I love there are protons ok and the resistance are acting as electrones? I love it!!. So a almost perfect cycles of time. For example it is possible to use instead of catodic protection use no metal materials.
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