Fractional Cassini Coordinates

Richard Herrmann

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arXiv · 1802.08142

Fractional Cassini Coordinates

Richard Herrmann

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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.

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Richard Herrmann. 2018-02-18. Fractional Cassini Coordinates. https://arxiv.org/abs/1802.08142

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