hmm. Let's assume that's ok ;). But even if so, as i calculated, it seems that cycloid isn't the solution of this equation. I don't have time to write it now but have you checked it also? I checked the parametric formulas:
x = r(t - sin(t)), y = r(1- cos(t))
hi
So, first let's say that our physical equivalent of the equations you've made is simple:
x(t) = t
To make it more adequate, let's denote that t varies from [0,1].
Variable n doesn't have any physical meaning - it's a parameter, as one said. So, as i read through the topic, it was just...
hi
the relation between ds, dx and dy :
ds = \sqrt{dy^2 + dx^2}
which you wrote in your first post is needed in deriving brachistrome because we need an independent variable to calculate. And, with that in mind, variable s is not a good one because it depends on x and y (which one is...