as before.

C.3 Roche Coordinates

Although the Roche potential is frequently used among binary astronomers, the Roche coordinates are less known. Roche coordinates, as investigated by Kitamura (1970) and Kopal(1970,1971), try to establish an(orthogonal) coordinate system (u, v, w) associated with the Roche potential Q in the circular case. The centers of both components are singularities of this coordinate system. The first coordinate is just equal to the Roche potential, i.e., u = Q. Unlike polar coordinates or other more frequently used coordinate systems which are related to the Cartesian coordinates by some explicit formulas, Roche coordinates cannot be described by closed analytical expression but can only be evaluated numerically. This property limits the practical use. Kopal & Ali (1971) and again Hadrava (1987) showed that it is not possible to establish a system of three orthogonal coordinates based on the Roche potential. The requirement that such coordinates exist [Cayley's (1872a, b) problem] imposes a necessary condition [the Cayley-Darboux equation (Darboux (1898)] which must be satisfied by the function Q. Hadrava (1987) defines generalized Roche coordinates in asynchronous rotation binaries with eccentric orbits and calculates them in the form of power series of the potential (3.1.77). His definition

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