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

[@anegativecoconut4940]

Three Blue One Flammy.

[@46pi26]

3b1b's cousin just now showed up

[@silasrodrigues1446]

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

[@BornInOz]

Another vote for brachistochrone!

[@swaree]

3Flammies1Papa

[@koenth2359]

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. v(t)=sqrt((dx/dt)^2+(dy/dt)^2) = sqrt((sin(t))^2 + (1-cos(t))^2) = sqrt(2-2cos(t)) = sqrt(2)•sqrt(1-cos(t)) [using the identity cos(t)=cos^2(t/2)-sin^2(t/2)=1-2sin^2(t/2)] = 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.

[@quahntasy]

Papa got a new dude on.

[@thelocalsage]

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

[@nestorv7627]

this turned out way better than i thought

[@acwern1703]

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

[@markusdemedeiros8513]

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

[@nickdalfarra3887]

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

[@cubicardi8011]

Subscribed to him! Is he german too?

[@liamcrawford9010]

Got a challenge for you PappaFlammy since you also like solving differential equations. Solve the hypergeometric equation x(1-x)y''+[2-(1+a+b)x]y'-aby=0

[@garrytalaroc]

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

[@alexismiller2349]

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

[@tonk6812]

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

[@wduandy]

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

[@SultanLaxeby]

And now the arclength of the cycloid?

[@icycounter-strikeandleague8431]

I read that as Xander Corvus

[@ApplyEval]

We miss you flammy!

[@ApplyEval]

@@PapaFlammy69 that was sooo long time ago! )

[@nicholasleclerc1583]

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

[@jeannelson8403]

That was nice

[@sansamman4619]

hmm, so.. there is no differential equation?

[@avinandannag7149]

Make a video on Hypo cycloid asteroid

[@XanderGouws]

Ye for sure. I've got a few other videos lined up but I'll definitely get around to it :D

[@avinandannag7149]

@@XanderGouws Gr8

[@cavver3523]

I love rolling things!

[@cavver3523]

Oh, and I subbed to this Xander boi!

[@mehtapuru]

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

[@XanderGouws]

I'll be making more soon - I've got a series on differential equations in the works :D

[@mehtapuru]

still waiting af

[@atrimandal4324]

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!

[@XanderGouws]

Yee :D

[@Fapmid]

[@fabulator2779]

Three black one brown

[@AllenHao-c8c]

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

[@OtiumAbscondita]

Oof them views are dropping ...

[@mihaiciorobitca5287]

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

[@mihaiciorobitca5287]

Flammable Maths yep i understand the concept ,i don't want to be spiteful,but what are useful for ??? I see entertaiment in thaf video and i appreciate you Xander,most of all this is the only one video on your channel...

[@codemagenta2681]

Mäddl loide!

[@xCorvus7x]

* daughters

[@rafaellisboa8493]

jesus what the fuck was that

[@PhasmidTutorials]