Fractional Cassini Coordinates

Abstract

Introducing a set $\{{\alpha }_i\}\in R$ 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 $R^3$ is investigated. The resulting asymmetric coordinate systems are well suited to solve corresponding two- and three center problems in physics.

10 pages, 4 figures