The aim of the present paper is to prove that the system of partial differential equations, which define a set of curvilinear coordinates ?, ?, ? that are orthogonal to the Roche equipotentials ?(r, ?, ?) 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 ? represents the potential.
- 1 - natural sciences ; 2 - physics & astronomy ; 3 - astronomy & astrophysics
- 1 - sciences appliquees, technologies et medecines ; 2 - sciences exactes et technologie ; 3 - terre, ocean, espace ; 4 - geophysique externe
- 1 - Physical Sciences ; 2 - Earth and Planetary Sciences ; 3 - Space and Planetary Science
- 1 - Physical Sciences ; 2 - Physics and Astronomy ; 3 - Astronomy and Astrophysics