The Brachistochrone Curve - Which theories apply?

In summary, the conversation revolves around a student asking for help with their physics exam project on creating a Brachistochrone curve. They mention writing a report and struggling to understand some of the theories behind the curve, specifically related to gravitational acceleration. The student has been using the internet for research but finds it difficult to understand due to being a non-native English speaker. They turn to asking for clarification in the conversation. The speaker advises the student to ask specific questions and provides some prompts for further discussion.
  • #1
FredLau
5
0
Hello,
I am doing a physics exam, where I have chosen to create a Brachistochrone curve, and perform various tests on it.
Furthermore, I also have to write a physics report, containing the theory behind the curve, but I am not 100% sure what some of the theories behind the curve are. I suppose it would apply to gravitational acceleration, since it is only affected by that force. But could anyone maybe explain to me just a bit more about the theory behind this curve? Thank you!

- Frederik L. Rasmussen
 
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  • #2
What did you find using the Internet?
 
  • #3
PeroK said:
What did you find using the Internet?
Don't worry, I have been looking on the internet!
But I am not a native English speaker, so a lot of the things I have been able to find has been somewhat hard for me to understand..
So I thought it would be easier to ask in here.
 
  • #4
FredLau said:
Don't worry, I have been looking on the internet!
But I am not a native English speaker, so a lot of the things I have been able to find has been somewhat hard for me to understand..
So I thought it would be easier to ask in here.

There must be a lot of available material with diagrams and which took hours to put together, so it's impossible for anyone here to do better than that. What we can do is answer specific questions about something you don't understand.

Where havve you got to in your project? Do you understand the problem? The idea behind the solution? What level of mathematics do you know?
 

Related to The Brachistochrone Curve - Which theories apply?

1. What is the Brachistochrone Curve?

The Brachistochrone Curve is a mathematical curve that represents the path between two points that a mass will take under the influence of gravity in the shortest amount of time. It was first proposed by Swiss mathematician Johann Bernoulli in 1696.

2. What theories apply to the Brachistochrone Curve?

The Brachistochrone Curve can be explained using theories from various branches of science, including classical mechanics, calculus, and differential geometry. Specifically, the curve can be derived using the principle of least action in classical mechanics and the calculus of variations.

3. What is the significance of the Brachistochrone Curve?

The Brachistochrone Curve is significant because it demonstrates the concept of the shortest time of descent, which is a fundamental principle in physics. It also serves as an example of the elegance and power of mathematical analysis and its ability to solve complex problems.

4. How is the Brachistochrone Curve used in modern science?

The Brachistochrone Curve is used in various applications, including engineering, physics, and computer graphics. It is used to optimize the path of motion for objects under the influence of gravity, such as roller coasters, pendulums, and projectiles. It is also used in the fields of robotics and computer animation to simulate realistic and efficient movement.

5. Are there any real-life examples of the Brachistochrone Curve?

Yes, there are several real-life examples that follow the Brachistochrone Curve, such as a marble rolling down a curved track, a skier following a curved path down a mountain, and a water slide at a theme park. These examples demonstrate the practical application and validity of the Brachistochrone Curve in real-world scenarios.

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