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On the plane curves whose curvature depends on the distance from the origin. (English) Zbl 1260.53012
Kielanowski, Piotr (ed.) et al., XXIX workshop on geometric methods in physics, Białowieża, Poland, June 27 – July 3, 2010. Selected papers based on the presentations at the workshop. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0861-6/hbk). AIP Conference Proceedings 1307, 112-118 (2010).
Summary: Here we suggest and exemplify a simple scheme for reconstruction of a plane curve if its curvature belonging to the class specified in the title by deriving explicit parametrizations of Bernoulli’s lemniscate and newly introduced co-lemniscate curve in terms of the Jacobian elliptic functions. The relation between them and the Bernoulli elastica are clarified.
For the entire collection see [Zbl 1234.81018].

53A04 Curves in Euclidean and related spaces
74K05 Strings