Solution to Brachistochrone Problem

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Discussion Overview

The discussion revolves around the Brachistochrone problem, specifically seeking a full solution as provided by Newton, along with explanations. Participants express varying levels of understanding and seek resources to clarify the solution process, touching on concepts like Fermat's principle and differential equations.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants request a full solution to the Brachistochrone problem as presented by Newton, indicating a desire for detailed explanations.
  • Others suggest that while the solution exists, participants should engage with the problem themselves to enhance understanding.
  • One participant expresses confusion regarding the solution provided on Wikipedia, particularly about the differential equations involved and their connection to the cycloid.
  • There is a mention of Fermat's principle and its application up to the differential equation stage, but a lack of clarity on how to solve it is noted.
  • Participants question the utility of simply restating the proof if it does not aid in understanding.

Areas of Agreement / Disagreement

Participants generally agree that the solution exists but disagree on the best way to understand it. There is no consensus on how to effectively communicate the solution or clarify the confusion surrounding it.

Contextual Notes

Participants express uncertainty about specific steps in the solution process, particularly regarding the differential equations and their implications. There is a reliance on external sources like Wikipedia, which some find insufficient.

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 !
 
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A Physics Enthusiast said:
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? :smile:
 
berkeman said:
Have you tried Googling your thread title? :smile:
Yes. But, I don't think I understand the solution of Newton provided in wikipedia.
:blushing:
 
A Physics Enthusiast said:
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.

A Physics Enthusiast said:
I don't think I understand the solution of Newton provided in wikipedia.

What are you having trouble understanding?
 
A Physics Enthusiast said:
Yes. But, I don't think I understand the solution of Newton provided in wikipedia.
:blushing:
If you can describe what you are having trouble understanding then we can probably help.
 
PeterDonis said:
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.

PeterDonis said:
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 ?
 
A Physics Enthusiast said:
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.

A Physics Enthusiast said:
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?
 
This might help:

 
  • #10
A Physics Enthusiast said:
I think I understand the Fermat's principle method (till the DE).

Which DE?
 
  • #11
A Physics Enthusiast said:
Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ?
A Physics Enthusiast said:
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?
 

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