|XXIX Workshop on Geometric Methods in Physics||27.06-03.07.2010|
On the Plane Curves Whose Curvature Depends on the Distance From the Origin
The plane curves specified in the title are studied in some
detail and examplified by deriving explicit parameterizations of
Bernoulli's Lemniscate and newly introduced Co-Lemniscate curve
in terms of the Jacobian elliptic functions. The relation
between them and with the Bernoulli elastica are clarified.