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Iwerlipse: Difference between revisions
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The Iwerlipse is the range of positions Mario can occupy when Mario is in the air and cannot turn, assuming the joystick input polling were continuous. It is defined as an area bounded by a shape drawn by the solution to optimizing a set of 2 differential equations. Due to the shape being similar to a superellipse (after Grassdigger brute forced for the solution in Mathematica), Pannenkoek2012 proposed calling this shape the "Iwerlipse" on August 2018 (pronounced eeverlipse /ˈivɜlɪps/) as a pun on the name of Iwer Sonsch, one of the people involved in this problem. | The '''Iwerlipse''' is the range of positions Mario can occupy when Mario is in the air and cannot turn, assuming the joystick input polling were continuous. It is defined as an area bounded by a shape drawn by the solution to optimizing a set of 2 differential equations. Due to the shape being similar to a superellipse (after Grassdigger brute forced for the solution in Mathematica), Pannenkoek2012 proposed calling this shape the "Iwerlipse" on August 2018 (pronounced eeverlipse /ˈivɜlɪps/) as a pun on the name of Iwer Sonsch, one of the people involved in this problem. | ||
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By plugging Iwer and Trex's equation to solve for x and y, we obtain the parametric equations, the solution to the Iwerlipse: | By plugging Iwer and Trex'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 = \pm \frac{v_xnt}{\sinh(t)} </math> | <math>x(n,t) = \pm \frac{v_xnt}{\sinh(t)} </math> | ||
<math>y(n,t) = v_in + \frac{a}{2}n^2\bigg(\coth(t)-\frac{t}{\sinh^2(t)}-\frac{D}{a}\bigg)</math> | |||
==See Also== | ==See Also== | ||
[[Straining]] | [[Straining]] | ||
==References== | ==References== | ||
Proof of the optimal straining equation :<br> | |||
[[File:IwerlipseProof.png]] | |||
[[Category:Mechanics]] | [[Category:Mechanics]] | ||