author: R. Herrmann

abstract:

Introducing a set {α_i}∈R of fractional exponential powers of focal distances an extension of symmetric Cassini-coordinates on the plane to the asymmetric case is proposed which leads to a new set of fractional generalized Cassini-coordinate systems. Orthogonality and classical limiting cases are derived. An extension to cylindrically symmetric systems in R³ is investigated. The resulting asymmetric coordinate systems are well suited to solve corresponding two- and three center problems in physics.

reference: arXiv:1802.08142