Jacobi Elliptic Function Intuition
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- čas přidán 3. 08. 2020
- In this video I look at the period of Jacobi Elliptic Functions, and some more of the analogies between elliptic functions and sine and cosine.
For more videos in this series, visit:
• Jacobi Elliptic Functions
Yet another hidden gem uncovered.
Thank you!
Great channel! I’m glad our algorithmic overlords have directed me here :)
Haha, well I'm glad you left such a kind comment!
Thanks so much for this video! I’ve been researching elliptic integrals and I was able to understand where E(k) comes from because I accidentally derived it, causing my research in the first place, but everywhere I looked, I wasn’t able to find a derivation of K(k) that felt as clear as this one!
How would you get numerical values from K(k)? Is the only way to approximate the integral?
Are there any "clear" definition of elliptic functions, kind of like what sinh = (e^x - e^-x) / 2 ?
elliptic integrals are inherently nonelementary, so there is no closed form except for special cases (such as k = 0 being a circle).
you'll actually get a different perspective if you watch the next video in this series, where the lecturer goes over differential equations that these elliptic functions satisfy. in particular, if you take y = sn(u, k), then y satisfies the nonlinear differential equation y'' = -(1 + k²)y + 2k²y³, which is a super ugly equation that resolves to the well known y'' = -y for the case of k = 0 (whose solutions are sine and cosine).
@@mossy8419 ty a lot !
Please tell me the application of elliptic integration in civil engineering
I don't know much about civil engineering, but you can use Elliptic Functions/Integrals to describe oscillations with an accuracy greater than that in the harmonic approximation.
@@physicsandmathlectures3289 For oscillation of a _pendulum_ specifically. Most other types of oscillation, such as RLC circuits or cavity resonators don't involve elliptic functions.