Undergrad Solution to Brachistochrone Problem

[A Physics Enthusiast]

Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ?

Or, any source about the same would be much helpful.

Thank you in advance !

 

[berkeman]

Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ?

Or, any source about the same would be much helpful.

Thank you in advance !

Have you tried Googling your thread title?

 

[A Physics Enthusiast]

Have you tried Googling your thread title?

Yes. But, I don't think I understand the solution of Newton provided in wikipedia.

 

[PeterDonis]

Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ?

The short answer to this is no. We can try to help you understand how to solve this problem, but you still have to do the work.

I don't think I understand the solution of Newton provided in wikipedia.

What are you having trouble understanding?

 

[Dale]

Yes. But, I don't think I understand the solution of Newton provided in wikipedia.

If you can describe what you are having trouble understanding then we can probably help.

 

[A Physics Enthusiast]

The short answer to this is no. We can try to help you understand how to solve this problem, but you still have to do the work.

LOL The proof is already there. All I need is a good resource to understand it.

What are you having trouble understanding?

Pretty much everything. I think I understand the Fermat's principle method (till the DE). But, no solution of the DE is provided in wikipedia to conclude that it is indeed a cycloid.

Mind referring a source ?

 

[PeterDonis]

The proof is already there. All I need is a good resource to understand it.

The best way to understand it is to solve it yourself. Having a known solution as a guide is often helpful, yes.

I think I understand the Fermat's principle method (till the DE). But, no solution of the DE is provided in wikipedia to conclude that it is indeed a cycloid.

Which Wikipedia article are you looking at?

 

[A Physics Enthusiast]

Which Wikipedia article are you looking at

https://en.m.wikipedia.org/wiki/Brachistochrone_curve?wprov=sfla1

 

[A.T.]

This might help:

 

[PeterDonis]

I think I understand the Fermat's principle method (till the DE).

Which DE?

 

[Vanadium 50]

Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ?

LOL The proof is already there. All I need is a good resource to understand it.

I'm confused. If we typed out the proof - which would be the same one in Wikipedia - how would that help you better understand it?