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File: 31 KB, 486x489, Double-pendulum-system.png [View same] [iqdb] [saucenao] [google]

Anonymous Mon Sep 11 01:19:13 2023 No.15735545 [Reply] [Original]

Is it possible to have a function that describes either the velocity or acceleration of the tip of a double pendulum as a function of time when released from certain given initial conditions?

>>	Anonymous Mon Sep 11 01:21:30 2023 No.15735548 >>15735545 >I need help with hw If you're looking for an analytic solution, it doesn't exist.

>>	Anonymous Mon Sep 11 01:23:38 2023 No.15735553 >>15735548 Not homework I just saw a double pendulum simulation on the internet and thought this question is interesting

>>	Anonymous Mon Sep 11 01:26:07 2023 No.15735556 >>15735548 proof?

>>	Anonymous Mon Sep 11 01:26:45 2023 No.15735560 >>15735545 yes

Anonymous Mon Sep 11 01:29:29 2023 No.15735567
File: 14 KB, 518x112, noanal.png [View same] [iqdb] [saucenao] [google]

>>15735556
The wiki article pretty much explains everything(en.wikipedia.org/wiki/Double_pendulum):
"It is not possible to go further and integrate these equations analytically, to get formulae for θ1 and θ2 as functions of time. It is however possible to perform this integration numerically using the Runge Kutta method or similar techniques." (picrel)

>>	Anonymous Mon Sep 11 01:34:34 2023 No.15735575 >>15735567 asking as a mathlet, can there be a proof that a particular PDE has no analytical solution?

>>	Anonymous Mon Sep 11 01:41:04 2023 No.15735585 >>15735545 P(theta_1 left of theta_2) / P(theta_1 right of theta_2) = 1

>>	Anonymous Mon Sep 11 01:47:38 2023 No.15735590 >>15735575 Yes, you can prove certain PDE's have no analytic solution using differential Galois theory.

>>	Anonymous Mon Sep 11 01:52:00 2023 No.15735599 >>15735590 particular ≠ certain

>>	Anonymous Mon Sep 11 01:58:58 2023 No.15735615 >>15735575 I actually dont know. (mathlet aswell)

>>	Anonymous Mon Sep 11 02:04:40 2023 No.15735624 >>15735567 to add on to this, its true that you cant get analytic solutions for θ1 and θ2. however you can use the small angle approximation to get good approximations, but that is the nature of chaotic motion though

>>	Anonymous Mon Sep 11 02:07:03 2023 No.15735629 >>15735624 I hate approximations. Those are for engineers. Mathematics is all about infinite precision.

Anonymous Mon Sep 11 02:18:17 2023 No.15735645

>>15735624
Computationally speaking, the approximation scheme you'd use really depends on the problem, for this I don't think small-angle approximation would be able to flesh out the chaotic behavior. Runge-Kutta is your best bet with these sort of things.

>>	Anonymous Mon Sep 11 02:46:21 2023 No.15735702 >>15735599 say what you mean instead of faggily nitpicking anon

>>	Anonymous Mon Sep 11 02:54:53 2023 No.15735715 >>15735702 "I can prove somthing" doesn't mean "I can't prove something else" happy?

>>	Anonymous Mon Sep 11 02:58:46 2023 No.15735722 File: 281 KB, 828x714, 1678268335474988.jpg [View same] [iqdb] [saucenao] [google] >>15735715 Not really, no See me after class

>>	Anonymous Mon Sep 11 03:02:51 2023 No.15735728 >>15735722 ok wow

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