I have come upon the curve with the following parametric equations:
$x(t)=\log(2+2\cos(t))/2$ $y(t)=t/2$
for $-\pi
Greg
I have come upon the curve with the following parametric equations:
$x(t)=\log(2+2\cos(t))/2$ $y(t)=t/2$
for $-\pi
Greg
This is more or less a reflected and shifted version of the so-called "catenary of equal resistance" (en français, sorry). Here is the paper where they were first studied.
Wikipedia gives a derivation for the equation of the catenary of equal resistance; in some references, this is also called the "catenary of uniform strength". See this for instance.