Brachistochrone problem with friction

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Discussion Overview

The discussion revolves around the brachistochrone problem with friction, focusing on specific steps in a mathematical demonstration. Participants seek clarification on the transitions between various equations presented in the article, particularly regarding the application of the Euler Lagrange equation and the integration of equations.

Discussion Character

  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the transition between equations (29) and (30) in the demonstration, suggesting that integration is involved.
  • Another participant confirms that equation (30) is the result of integrating equation (29), implying a first-order relationship.
  • A different participant questions the application of the Euler Lagrange equation to the integrand in equation (28), stating that it does not seem to simplify to equation (29).

Areas of Agreement / Disagreement

There is no consensus on the clarity of the mathematical steps involved, as participants express differing levels of understanding and seek assistance on specific transitions between equations.

Contextual Notes

Participants note specific steps in the demonstration that are unclear, particularly the integration process and the application of the Euler Lagrange equation, without resolving these issues.

janonus
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Hey,
I am doing some research on the brachistochrone problem WITH frictions. I found the following demonstration on the web.
The beginning is ok. But I can't understand how the managed to pass between (29) and (30) and between (30) and ((32), (33)).

If someone could help me, it would be very nice !
thanks :)

The link to the article : http://mathworld.wolfram.com/BrachistochroneProblem.html
 
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To go from 29 to 30, it is pretty clear that they have integrated one time. Eq(29) is second order while eq(30) is first order. What you need to do is convince yourself that 30 is indeed the result of integrating 29.
 
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Yeah, I got it !
Tanks for your help Dr.D ! :smile:
 
Hi, not sure if it is ok to revive an old question, I am also having trouble following some of the steps in this demonstration, in particular steps (28) to (29). I know what the Euler Lagrange equation is, but applying it to the integrand in (28) does not appear to simplify to (29). Would anyone be able to help me with this?
 

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