Equations of a Cycloid: A Derivation - feat. Xander Gouws

I hope you are going to enjoy this great presentation by Xander! =)

Please leave your constructive criticism in the comments, everyone's giving it their best! =)

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[silasrodrigues]

One of the most easiest understandable explanations about cycloid I've ever seen! How about the brachistochrone problem?

[koenth]

Well done Xander, nice animations
So, x=t-sin(t), y=1-cos(t)
Now only the fun starts: e.g. find the arc length of a cycloid corresponding to 1 full revolution.

= sqrt((sin(t))^2 + (1-cos(t))^2) = sqrt(2-2cos(t)) = sqrt(2)•sqrt(1-cos(t))
[using the identity
= sqrt(2)•sqrt(2sin^2(t)) = 2|sin(t/2)|
Sin is nonnegative on the interval of interest, so just drop the absolute value

Now the arc length is the integral of v which is -4cos(t/2), for t from 0 to 2pi
-4(cos(pi)-cos(0)) = -4(-1-1) = 8.

[thelocalsage]

This actually cleared up a lot about roulette parametrization that I didn’t understand in under three minutes!

[nestorv]

this turned out way better than i thought

[markusdemedeiros]

Interesting how the y value is the derivative with respect to t of the x value.

[acwern]

Papa Euleroid arrived today. Played him some Space Rock. Punched some Mare's Tail. Fun times. Best purchase

[nickdalfarra]

Its yer boi Bernoulli, comin at you with the fastest path of decent under a constant gravitational field

[liamcrawford]

Got a challenge for you PappaFlammy since you also like solving differential equations. Solve the hypergeometric equation

[tonk]

Next for cardiode ❤and lemniscate🌸....🙂🙂🤗🤗😂

[garrytalaroc]

Wow that was quick. Wasn't expecting that. Our class used lagrange and it was tricky.

[alexismiller]

Nice dude yes nice I wanted to see this even before you made it thanks papa flammy I also hate commas

[wduandy]

Flammy, what song did you use on the beginning of the video?

[mehtapuru]

Holy shit this guy's good. Why doesn't he have more videos?

[atrimandal]

So once the flammily is large enough to accidentally inbreed, will the offsprings of those unions be born with an Euler T Shirt signed by Papa? 😂😂
The video was pretty great tbh!

[nicholasleclerc]

Maybe THIS guy will answer my question of how to derive ballistic equations with atmospheric friction F so that:
||F||=b*||v(t)||^2;
Where b=(fluid density)*(Cross-section area)*(Friction coefficient)/2
And v(t)=Velocity vector of object

[sansamman]

hmm, so.. there is no differential equation?

[AllenHao-cc]

Cound we have some discrete math, like generating equation or something 😄

[mihaiciorobitca]

Oh guuuys...i love the content that you present but would be nice to add a little example in real life :(((