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On the integrability of the Roche coordinates

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Abstract

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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Authors and Affiliations

  1. Dept. of Astronomy, University of Manchester, England

    Zdeněk Kopal & A. K. M. Sekender Ali

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  1. Zdeněk Kopal
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  2. A. K. M. Sekender Ali
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Kopal, Z., Sekender Ali, A.K.M. On the integrability of the Roche coordinates. Astrophys Space Sci 11, 423–429 (1971). https://doi.org/10.1007/BF00649635

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  • DOI: https://doi.org/10.1007/BF00649635

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