What are some ways to further explore the brachistochrone problem?

In summary, the student is seeking help with the brachistochrone problem in their second year of studying math, physics, and informatics. They have already made some progress, including finding the parametric equation of the cycloid and writing programs to draw the curve. However, they are unsure of how to continue and are seeking indications for further research. They mention the possibility of exploring curves generated by other geometric figures, friction actions in physics, and using informatics, but are not sure how to apply these ideas to the problem. They also apologize for any language errors as they are still learning English.
  • #1
janonus
3
0

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 !
 
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  • #3
janonus said:

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.
 

1. What is the Brachistochrone problem?

The Brachistochrone problem is a mathematical challenge that asks for the shortest time it takes for a particle to travel between two points under the influence of gravity. This problem was first posed by Johann Bernoulli in 1696 and has since been solved by various mathematicians and physicists.

2. How is the Brachistochrone problem solved?

The Brachistochrone problem can be solved using the calculus of variations, which involves finding the path that minimizes the time of travel. This solution is known as the Brachistochrone curve, which is a cycloid. The cycloid is a curve traced by a point on a circle as it rolls along a straight line.

3. What is the significance of the Brachistochrone problem?

The Brachistochrone problem is significant because it not only demonstrates the power of mathematical methods but also has practical applications in various fields. For example, it is used in engineering and physics to optimize the time of travel for objects under the influence of gravity.

4. Are there any real-life examples of the Brachistochrone problem?

Yes, there are several real-life examples of the Brachistochrone problem. One example is the path taken by a skier going from point A to point B on a mountain. Another example is the path of a rollercoaster, which is designed to have the shortest time of travel while still providing an exhilarating experience for riders.

5. Can the Brachistochrone problem be generalized to higher dimensions?

Yes, the Brachistochrone problem can be generalized to higher dimensions. In fact, the problem can be extended to any number of dimensions and is known as the n-dimensional Brachistochrone problem. However, the solution becomes more complex and difficult to visualize as the number of dimensions increases.

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