#newton

mkwadee@diasp.eu

A couple of weeks ago, I posted an #animation of a point on a circle generating a #cycloid.
Generating a cycloid

If you turn the curve "upside down", you get the #BrachistochroneCurve. This curve provides the shortest travel time starting from one cusp to any other point on the curve for a ball rolling under uniform #gravity. It is always faster than the straight-line travel time. This is an interesting problem in #ClassicalMechanics and exercised luminaries like #Newton and #Euler. I think the latter's use of the #CalculusOfVariations is a stroke of genius.

Anyway, the #animation took a bit of thought as it requires a bit of #Mechanics, some #Integration and is made a bit more tricky as the curve is multi-valued and so you need to treat different branches separately. The #AnimatedGif was produce with #WxMaxima.

For some reason that I can't fathom, I'm not finding it possible to upload the graphic and so if you want to see it, please use the link below.
https://drive.google.com/file/d/1edcZnZ_uiaQOQrFB03XHslNUVCmxcSut/view?usp=drive_link

#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus

deutschewelle@squeet.me

Warum wir die besten Ideen unter der Dusche haben | DW | 26.10.2022

Vielleicht sehen auch Sie manchmal einfach nur so aus dem Fenster und lassen Ihren Gedanken freien Lauf? Genau das sind die Momente, in denen sich oft außergewöhnliche Erkenntnisse und brillante Ideen entwickeln.#Epiphanie #Erleuchtung #Einstein #Archimedes #Newton
Warum wir die besten Ideen unter der Dusche haben | DW | 26.10.2022

magdoz@diaspora.psyco.fr