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.