- #1
physics_cosmos
- 6
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This Wolfram Alpha Page contains a derivation of the parametric form of the brachistochrone curve that result from either assuming friction or its absence.
I am asking for help understanding how the solution to the differential equation obtained from applying the Euler-Lagrange equation to the integrand of the the integral representing the total time of descent is obtained. This differential equation can be found on step (30) of the page. I am asking for help in understanding the next step, how setting dy / dx = cot(theta/2) results in the given parametric forms for x and y (in terms of theta), as given in steps (32) and (33).
I am asking for help understanding how the solution to the differential equation obtained from applying the Euler-Lagrange equation to the integrand of the the integral representing the total time of descent is obtained. This differential equation can be found on step (30) of the page. I am asking for help in understanding the next step, how setting dy / dx = cot(theta/2) results in the given parametric forms for x and y (in terms of theta), as given in steps (32) and (33).