Integration theory for the restricted problem of three axisymmetric bodies. (English) Zbl 0699.70011
Summary: In this paper the circular planar restricted problem of three axisymmetric ellipsoids \(S_ i(i=1,2,3)\), such that their equatorial planes coincide with the orbital plane of the three centres of masses, be considered. The equations of motion of infinitesimal body \(S_ 3\) be obtained in the polar coordinates. Using iteration approach we have given an approximation for another integral, which independent of the Jacobian integral, in the case of P-type orbits (near circular orbits surrounding both primaries).
MSC:
| 70F07 | Three-body problems |
Keywords:
circular planar restricted problem of three axisymmetric; ellipsoids; equatorial planes; iteration approach; Jacobian integral; circular planar restricted problem of three axisymmetric ellipsoidsReferences:
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