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Qmechanic ♦
Qmechanic ♦
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I have watched videos on the Brachistochronebrachistochrone problem and how to find the quickest path a particle can take between two points. However they never gave an exact function for the path. I thought of using the least action principle but it seems as if it just gives you an idea of how to solve it and doesn't give the exact answer. So what is the exact function for the brachistochrone between points $(x_1, y_1)$ and $(x_2, y_2)$?

I have watched videos on the Brachistochrone and how to find the quickest path a particle can take between two points. However they never gave an exact function for the path. I thought of using the least action principle but it seems as if it just gives you an idea of how to solve it and doesn't give the exact answer. So what is the exact function for the brachistochrone between points $(x_1, y_1)$ and $(x_2, y_2)$?

I have watched videos on the brachistochrone problem and how to find the quickest path a particle can take between two points. However they never gave an exact function for the path. I thought of using the least action principle but it seems as if it just gives you an idea of how to solve it and doesn't give the exact answer. So what is the exact function for the brachistochrone between points $(x_1, y_1)$ and $(x_2, y_2)$?

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Kamal Saleh
Kamal Saleh
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Exact function for the brachistochrone

I have watched videos on the Brachistochrone and how to find the quickest path a particle can take between two points. However they never gave an exact function for the path. I thought of using the least action principle but it seems as if it just gives you an idea of how to solve it and doesn't give the exact answer. So what is the exact function for the brachistochrone between points $(x_1, y_1)$ and $(x_2, y_2)$?