# Bipolar coordinates

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The numbers and which are connected with the Cartesian orthogonal coordinates and by the formulas where . The coordinate lines are two families of circles with poles and and the (half-c)ircles orthogonal with these . Figure: b016470a

The Lamé coefficients are: The Laplace operator is: Bipolar coordinates in space (bispherical coordinates) are the numbers and , which are connected with the orthogonal Cartesian coordinates and by the formulas:   where . The coordinate surfaces are spheres ( ), the surfaces obtained by rotation of arcs of circles ( ) and half-planes passing through the -axis. The system of bipolar coordinates in space is formed by rotating the system of bipolar coordinates on the plane around the -axis.

The Lamé coefficients are:  The Laplace operator is:  How to Cite This Entry:
Bipolar coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bipolar_coordinates&oldid=11655
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article