What are some ways to further explore the brachistochrone problem?

[janonus]

Homework Statement

Hi I'm in second year of study in Math, Physic and Informatic and I require some help.
I began a work on the brachistochrone problem. It's really interesting and I already found lot of things (the equation of the cycloid by the Bernoulli's method, I wrote some programs which draw the curve between two point,... )
But after this first researchs and results I don't know how to continue... Could you help me, give me some indication to go further ?


2. Homework Equations
Parametric equation of the cycloid

The Attempt at a Solution

Further in math : curves generate by other geometric figures ?
Further in physics : friction actions ? Speed font ion of the time ?
Further in Informatic : No idea...

Thank's for your help :)

PS : excuse me for my English... I'm French and I'm still learning !

 

[jedishrfu]

Have you looked at a classical physics book and how to use the calculus of variations to solve the problem?

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

Please be aware that we can't provide the solution or show you how to do it. We can only provide hints based on the work you've shown.

 

[rude man]

Homework Statement

Hi I'm in second year of study in Math, Physic and Informatic and I require some help.
I began a work on the brachistochrone problem. It's really interesting and I already found lot of things (the equation of the cycloid by the Bernoulli's method, I wrote some programs which draw the curve between two point,... )
But after this first researchs and results I don't know how to continue... Could you help me, give me some indication to go further ?


2. Homework Equations
Parametric equation of the cycloid

The Attempt at a Solution

Further in math : curves generate by other geometric figures ?
Further in physics : friction actions ? Speed font ion of the time ?
Further in Informatic : No idea...

Thank's for your help :)

PS : excuse me for my English... I'm French and I'm still learning !

My old Housner & Hudson, Applied Mechanics - Dynamics covers the subject. You might also want to read my Insight blog Brachistochrone Subway! and attendant comments in this forum.