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About The Lagrangian in the simulation of Earth orbiting the Sun #1

Closed kinow closed 3 years ago

kinow commented 3 years ago

Hi!

Thanks for the blog post. I'm working on some CSS/JS animation, and researching ways to do a smooth orbit style, and have found your blog post .

Under the The Lagrangian section, there's a phrase that I think is right, but I think the figure next to it is wrong (?)

We will find the equations of motions using the Lagrangian, which is the kinetic energy minus the potential energy of the Sun-Earth system:

But your figure uses the plus sign.

image

I checked the Lagranian mechanics Wikipedia page, and I think what you said is right, but the formula has the wrong sign.

Thanks! Didn't find the source of the image, otherwise would have submitted a PR :+1: Bruno

kinow commented 3 years ago

Oh, d'oh. Sorry. I was reading the other document with the derivation used in another formula, and noticed you also used +.

Then realized the variable replaced was negative, hence the + sign. Sorry the noise!