On the Integrability of the Roche Coordinates

Details On the Integrability of the Roche Coordinates On the Integrability of the Roche Coordinates

Jun 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971ap%26ss..11..423k&link_type=abstract

Astrophysics and Space Science, Volume 11, Issue 3, pp.423-429

Astronomy and Astrophysics

Astrophysics

7

Scientific paper

The aim of the present paper is to prove that the system of partial differential equations, which define a set of curvilinear coordinates ξ, η, ζ that are orthogonal to the Roche equipotentials ξ(r, θ, ϕ) incorporating the effects of both rotationaland tidal distortion, does not admit of any formal integrals; and can be solved only numerically in an asymptotic manner. This fact is related with analytic properties of the problem of three bodies, in which ξ represents the potential.

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