I Is it possible to solve for “t?”

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The discussion centers on the formula A=-(B/2(pi-t+sin(t)))(1-cos(t)), which is used to determine the quickest route between two horizontal points. While A and B can be calculated when t is known, finding t analytically when A and B are given is deemed nearly impossible due to the complexity of the equation, which involves t both inside and outside trigonometric functions. Numerical methods, such as the Newton-Raphson technique, can provide approximate solutions, but multiple solutions for t exist, complicating the determination of a unique answer. The conversation also touches on the irrational nature of t when A and B are rational, and the implications of calculating the quickest path, suggesting that it may require infinite precision. Ultimately, while numerical solutions can be achieved, an exact analytical solution for t remains elusive.
  • #91
pbuk said:
I don't think you can. In any case the mathematical solution is useless, this is an engineering problem and yopu need to non-neglect all the neglected variables.

The resulting problem is only solvable (but trivially solvable) by computational methods.

There is nice approximate form of solution starting on bottom of 332 here:
https://www.jstor.org/stable/2974953?seq=5#metadata_info_tab_contents

Also, I think this is not an engineering problem, but quite a purely mathematical problem!
 
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  • #92
There's tons of open sourced info about this in Musk's hyperloop project, no need to pursue it further here.
 
  • #93
pbuk said:
There's tons of open sourced info about this in Musk's hyperloop project, no need to pursue it further here.
... where still the mathematical formula should be discussed, and not the physical system which led to it.

If someone wants to open a new thread about Hyperloop, please feel free to do so. Contact a mentor if you want some of the late posts here to be moved into the new thread in order to get it started.
This one will be closed.
 
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