Elliptical functions appears also in electrostatics and magnetostatics. Check in Jackson's classical electrodynamics, chapters 3 and 5. (Note: Green functions are involved, also Bessel functions in cylindrical coordinates and expansions in terms of Legendre polynomials in spherical coordinates.)
But if we want to measure orbits and circumference of Earth we probably need this \frac{\pi}{2}\cdot\sum\limits_{n=0}^{\infty}\frac{1}{1-2n}\cdot {2n \choose n}^2\cdot\left(\frac{k}{4} ight)^{2n}
Bro you just cleared my one the most pondering doubt. One day i was just solving the motion of pendulum ; i was thinking to do it just from kinematics algebra and encountered this integral which i wasn't able to do. Searched on yt i ffound that this integral is unsolvable then i questionined on the existence of motion of pendulum . From thn onwards i was searching for it.
Hi, Interesting approach to calculate the period of the pendulum starting from a certain angle and assuming zero friction, but without the assumption of the small angle. "ok, cool" : 0:30 , 1:24 , 3:09 , 8:57 , 9:57 , 12:24 , 19:04 , "terribly sorry about that" : 5:09 , 13:19 .
@@maths_505 To be honest, you said once "ok" (without "cool") 🙂 . I also counted Michael Penn's usual formulas, but he doesn't typically have as many formulas as you, except of course his famous "and that's a good place to stop" at the end.
Absolutely fantastic video, you explained the elliptic integral in such a simple way, and explained the step of normalisation of the T/period integral well - I previously never really understood the motivation of that last substitution. Great H/W exercise too, I got (omega-bar)/sqrt(2) ! I feel that the identity that came before it with the gamma functions looked cooler though - it was like the Euler identity for special functions 😍 My only other comment is that at 1:15 you state that the pendulum executes SHM, but the whole point of using elliptic integrals is that it isn't SHM. Or was that a meta-joke referring to how physicists just model everything as SHM whether it's SHM or not? 😂 I feel like this level of explanation would really suit an advanced high-school student, I really hope for more content like this on elliptic functions 😊
Thanks bro. Yeah it is SHM because acceleration is still proportional to displacement. Modelling this system in the form of a second offer differential equation (using an FBD on the mass m) will show that explicitly.
@@maths_505 😮 I immediately got my pen and paper and frantically tried deriving the equation. But for the x-displacement I got: x'' = -(gx/l^2)*(l^2-x^2) For s (arc length), I got: s'' = -g*sin(s/l) For y I got something even more horrible! Which direction/displacement does it execute SHM in? I'm really curious
@@edmundwoolliams1240 try the polar coordinates. Rather, now that I think of it, for the polar angle φ I think you'll get an equation showing it proportional to sin(φ) and not exactly φ. So strictly speaking, I should not have said SHM but simply oscillatory motion. Thanks for sparking the discussion mate. Although everything is pretty much a harmonic oscillator, one should be more rigorous when teaching so I'll be sure to avoid it next time 😂
@@maths_505 It was something extremely minor, I was just being a stickler 😂 It basically is SHM, I only wanted to point it out because if it were genuine SHM then we could just read off the period directly from the ODE and we wouldn't get to use the cool elliptic integrals (which most treatments of the simple pendulum sadly never go into detail about!) Ever since I first learned it in high school, I've always found the simple pendulum so mysterious too: it looks, feels, and moves like SHM, but it isn't, and the equation describing it is inexplicably so much harder to solve!
Более интересная и полезная задача как организовать класс для вычисления этой функции с точностью 16D b сложностью вычисления многочлена степени N. Увы единого подхода решения этой задачи нет. Вообще в математике надо совершенствовать искусство численного интегрирования с высокой точностью и низкой сложностью вычислительных ресурсов ПК!
Since this is the first time one of the 3 and a half ladies who watch this channel has ever made a request I shall gladly oblige 😂 I am pretty occupied these days and have a long list of integral requests so I'll return to the list as soon as I get some time to breath (integration sounds like a viable replacement for breathing 😭😂)
But if at the bottom velocity is zero, then it will NOT swing any further! I think, all you can say is that the addition of T + U is just some constant c, and unless provided other details, we can NOT conclude c = mgl cos phi zero. Correct?
U dedicated yourself just so we could understand integral calculus
RESPECT
Love from India🇮🇳
@@rudransh118 thanks bro
been following for months and now I'm starting to see myself knowing the next step ahead!! it's so cool
Elliptical functions appears also in electrostatics and magnetostatics. Check in Jackson's classical electrodynamics, chapters 3 and 5. (Note: Green functions are involved, also Bessel functions in cylindrical coordinates and expansions in terms of Legendre polynomials in spherical coordinates.)
Always ugly af but I guessed it's just not my thing
Its a kamaal approach
Is he a Muslim?
Because Kamal is an Arabian name
Chamar approach when
@@asserhaitham8067 yeah bro I'm Muslim alhamdullilah
@@strikerstone Have some respect man
@@chaitanyasinghal1098 for whom?
We can expand it via binomial expansion and then use reduction formula derived by parts and we avoid Beta function and stuff like that
My solution expressed as series in latex
\frac{\pi}{2}\cdot\sum\limits_{n=0}^{\infty}{2n \choose n}^2\cdot\left(\frac{k}{4}
ight)^{2n}
But if we want to measure orbits and circumference of Earth we probably need this
\frac{\pi}{2}\cdot\sum\limits_{n=0}^{\infty}\frac{1}{1-2n}\cdot {2n \choose n}^2\cdot\left(\frac{k}{4}
ight)^{2n}
Love that boi cause it's closely related to elliptic curves
Bro you just cleared my one the most pondering doubt. One day i was just solving the motion of pendulum ; i was thinking to do it just from kinematics algebra and encountered this integral which i wasn't able to do. Searched on yt i ffound that this integral is unsolvable then i questionined on the existence of motion of pendulum . From thn onwards i was searching for it.
Yess!! The top integral G is back!
Hello my friend.
Yeah I've been pretty occupied this past week which is why I haven't been able to make videos. More uploads to follow Insha'Allah.
@@maths_505 It was well worth the wait my friend! I'm glad that you took your time to make something great 👍🏻 Looking forward to the next one
Lets fking goooooooooooooooo
I NEEDED THIS ONE
Whoever decided to use K, K', k, and k' all at the same time for elliptic integrals is evil. Thank you so much for not doing that.
Sir , is it even possible to solve
an integral from minus 1 to 1 of
(sin x /arcsin X)
It'll definitely converge but I'm not sure it'll have a nice closed form or not
@maths_505 hope u give it a try I'm interested in that integral🥺
Brilliant! I hve been waiting for one of this ones for a while! Great video! :)
Thank you for this featured effort.
Hi,
Interesting approach to calculate the period of the pendulum starting from a certain angle and assuming zero friction, but without the assumption of the small angle.
"ok, cool" : 0:30 , 1:24 , 3:09 , 8:57 , 9:57 , 12:24 , 19:04 ,
"terribly sorry about that" : 5:09 , 13:19 .
Terribly sorry about only giving 2 instances of me saying terribly sorry about that 😂
@@maths_505 To be honest, you said once "ok" (without "cool") 🙂 .
I also counted Michael Penn's usual formulas, but he doesn't typically have as many formulas as you, except of course his famous "and that's a good place to stop" at the end.
Absolutely fantastic video, you explained the elliptic integral in such a simple way, and explained the step of normalisation of the T/period integral well - I previously never really understood the motivation of that last substitution.
Great H/W exercise too, I got (omega-bar)/sqrt(2) !
I feel that the identity that came before it with the gamma functions looked cooler though - it was like the Euler identity for special functions 😍
My only other comment is that at 1:15 you state that the pendulum executes SHM, but the whole point of using elliptic integrals is that it isn't SHM.
Or was that a meta-joke referring to how physicists just model everything as SHM whether it's SHM or not? 😂
I feel like this level of explanation would really suit an advanced high-school student, I really hope for more content like this on elliptic functions 😊
Thanks bro.
Yeah it is SHM because acceleration is still proportional to displacement. Modelling this system in the form of a second offer differential equation (using an FBD on the mass m) will show that explicitly.
@@maths_505 😮 I immediately got my pen and paper and frantically tried deriving the equation. But for the x-displacement I got:
x'' = -(gx/l^2)*(l^2-x^2)
For s (arc length), I got:
s'' = -g*sin(s/l)
For y I got something even more horrible!
Which direction/displacement does it execute SHM in? I'm really curious
@@edmundwoolliams1240 try the polar coordinates. Rather, now that I think of it, for the polar angle φ I think you'll get an equation showing it proportional to sin(φ) and not exactly φ. So strictly speaking, I should not have said SHM but simply oscillatory motion. Thanks for sparking the discussion mate. Although everything is pretty much a harmonic oscillator, one should be more rigorous when teaching so I'll be sure to avoid it next time 😂
@@maths_505 It was something extremely minor, I was just being a stickler 😂 It basically is SHM, I only wanted to point it out because if it were genuine SHM then we could just read off the period directly from the ODE and we wouldn't get to use the cool elliptic integrals (which most treatments of the simple pendulum sadly never go into detail about!)
Ever since I first learned it in high school, I've always found the simple pendulum so mysterious too: it looks, feels, and moves like SHM, but it isn't, and the equation describing it is inexplicably so much harder to solve!
Cool 😃
i think this is my favorite video you’re made
Your explanation is nice.is complete elliptic integral has logarithmic singularity at k=1?
man u should make more physics related videos
Great video but do a video on integral(sqrt(1+sin^2theta)) from 0 to pi/2.
In 8:32, shouldn't the order of limits for phi be the other way around?
K(1/√2) = √2 K(i) = (1/√2)ϖ
ಠ﹏ಠ(´⊙ω⊙`)！
lemniscate constant🎉
Deeeng I did not see that Beta function coming.
very cool
Более интересная и полезная задача как организовать класс для вычисления этой функции с точностью 16D b сложностью вычисления многочлена степени N. Увы единого подхода решения этой задачи нет. Вообще в математике надо совершенствовать искусство численного интегрирования с высокой точностью и низкой сложностью вычислительных ресурсов ПК!
конечно интересный вариант
Hi bro , this time can you do the integral from e to 0 for : ln(1-ln(x)) ,its ez and give two beautiful constants , just try it
Since this is the first time one of the 3 and a half ladies who watch this channel has ever made a request I shall gladly oblige 😂 I am pretty occupied these days and have a long list of integral requests so I'll return to the list as soon as I get some time to breath (integration sounds like a viable replacement for breathing 😭😂)
xD😂😂 , but I am not a lady
Is the answer (e)*(euler mascheroni) constant ?
What’s the physical sense of evaluated at i?
I think you have to just imagine it.
do the double pendulum
Okay
@@maths_505 cool
But if at the bottom velocity is zero, then it will NOT swing any further! I think, all you can say is that the addition of T + U is just some constant c, and unless provided other details, we can NOT conclude c = mgl cos phi zero. Correct?
Wrong
The velocity is maximum at the bottom.
@maths_505 Yes, and therefore T is not zero at bottom. Hence total energy at bottom is not just - mgl cos phi zero, but T max + - mgl cos phi zero!
w video topci
Non ho capito perché hai messo n=i?
puro svago
yaaaaaas at laaaaast haha haha AHAHAHAHAHAH
I wanna be the first to comment. Nice job