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Anonymous Wed 12 Feb 16:55:10 2020 No.11379799 View Reply Original Report

Quoted By: >>11380005 >>11380293

Could someone plz ,walk me through or help me understand Jakob Bernoulli's solution in this article ?

https://en.m.wikipedia.org/wiki/Brachistochrone_curve

What kind of implicit differentiation is this ? You don't learn it in mainstream calculus courses.

Anonymous

Anonymous Wed 12 Feb 2020 17:07:27 No.11379820 Report

Quoted By: >>11379835 >>11379850 >>11379880 >>11379894

you don't learn this in mainstream calculus courses because its fucking dogshit crap made up by idiots

this is quite possibly one of the worst things I've ever seen, at least the majority of these ridiculous differential arguments used by physishits can be made rigorous with differential forms but the $2dsd^2s$ is atrocious.

Anonymous

Anonymous Wed 12 Feb 2020 17:12:39 No.11379835 Report

Quoted By:

>>11379820
That can still really easily be described using differential forms there's nothing atrocious. If you want something easier to grock just work with small displacements and expand up to second order before taking the limit.

Anonymous

Anonymous Wed 12 Feb 2020 17:25:37 No.11379850 Report

Quoted By: >>11379858

>>11379820
I understand that there is some controversy surrounding the d operator but i just want someone to help me understand the argument being presented
I don't care about rigor

Anonymous

Anonymous Wed 12 Feb 2020 17:32:01 No.11379858 Report

Quoted By: >>11379861

>>11379850
I thought he just assumed that if you treat the path of the light beam, it should obey snells law the entire way.

Anonymous

Anonymous Wed 12 Feb 2020 17:33:57 No.11379861 Report

Quoted By:

>>11379858
That's Johan Bernoulli's solution , Jakob did some crazy shit , taking derivatives of ds and dx, God know what's that supposed to mean.

Anonymous

Anonymous Wed 12 Feb 2020 17:44:15 No.11379880 Report

Quoted By:

>>11379820
If you think about differentials the oldschool way before modern rigorous definitions were used, you actually get a much more intuitive understanding of analysis that God-tier analysts like Euler and Newton had, and you'll still be correct 99% of the time.

Anonymous

Anonymous Wed 12 Feb 2020 17:44:50 No.11379881 Report

Quoted By:

I suppose we are implicitly differentiating with respect to time ?? to obtain

2ds d^2 s = 2dx d^2 x

Anonymous

Anonymous Wed 12 Feb 2020 17:51:57 No.11379894 Report

Quoted By:

>>11379820
just write "+ higher order terms" after every expression and suddenly everything becomes rigorous

Anonymous

Anonymous Wed 12 Feb 2020 19:09:42 No.11380005 Report

Quoted By: >>11380025

>>11379799
i forget but the other bernoulli's light solution is the most based from what I remember

Anonymous

Anonymous Wed 12 Feb 2020 19:25:16 No.11380025 Report

Quoted By: >>11380175

>>11380005
It's not really light , it's just snell's law

Anonymous

Anonymous Wed 12 Feb 2020 20:33:51 No.11380175 Report

Quoted By:

>>11380025
>snells law
youre even more retarded than my original post. I said light because its well known that light takes the path of least action.

Anonymous

Anonymous Wed 12 Feb 2020 21:43:49 No.11380293 Report

Quoted By:

>>11379799
It's confusing because he uses 2 d's when he could really use 1.
Let y1, y2 be constant and v1, v2 be the constant speeds in those regions.
Let x1 + x2 = X be constant (x1 and x2 can vary). This means dx1 = -dx2
(s1)/(t1) = v1 is constant. (s2)/(t2) = v2 is constant.
(ds1) = (v1)(dt1) and (ds2) = (v2)(dt2).
Since t1 + t2 = T is minimized, dt1 + dt2 = 0 = (ds1)/(v1) + (ds2)/(v2).

(s1)^2 = (x1)^2 + (y1)^2 ----> (ds1) = (x1)(dx1)/(s1)
(s2)^2 = (x2)^2 + (y2)^2 ----> (ds2) = (x2)(dx2)/(s2)
Divide by the v's and add to get dt1 + dt2 = 0.
(x1)(dx1)/(v1*s1) + (x2)(dx2)/(v2*s2) = 0
Since dx1 = -dx2, divide by dx1 to get (x1)/(v1*s1) - (x2)/(v2*s2) = 0.

Anonymous

Anonymous Thu 13 Feb 2020 06:53:40 No.11381441 Report

Quoted By:

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