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Iwerlipse: Difference between revisions
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The problem was posed by | The problem was posed by DeRockProject as a curiosity, and it became relevant to the ABC challenge a few times before being solved through some other means. | ||
Iwer stated on April 2018 that optimal straining for the Air_no_Turn action is <math>\text{dyaw}(t,r) = \text{acotan}(0.15r*t) </math>. | Iwer stated on April 2018 that optimal straining for the Air_no_Turn action is <math>\text{dyaw}(t,r) = \text{acotan}(0.15r*t) </math>. | ||
On October 2019, | On October 2019, Silverstrawb provided a full analytical proof for Iwer's claim, using a generalized 2nd-order Euler-Lagrange equation. | ||
By plugging Iwer and | |||
By plugging Iwer and Silverstrawb's equation to solve for x and y, we obtain the parametric equations, the solution to the Iwerlipse after <math>n</math> frames: | |||
<math>x(n,t) = \pm \frac{v_xnt}{\sinh(t)} </math> | <math>x(n,t) = \pm \frac{v_xnt}{\sinh(t)} </math> | ||
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[[Straining]] | [[Straining]] | ||
==References== | ==References== | ||
Proof of the optimal straining equation :<br> | |||
[[File:IwerlipseProof.png]] | |||
[[Category:Mechanics]] | [[Category:Mechanics]] | ||