Motion near the unit circle in the three-body problem
The author investigates the motion near the unit circle \((r=1)\) by expanding the Lagrangian of the restricted problem up to different orders of \(\varepsilon\) \((r=1 +\varepsilon,\;\varepsilon\ll 1)\). The Clohessy-Wiltshire equations are analysed in perturbed and unperturbed form, and a new symmetric property with respect to the unit circle is discovered. It is also revealed that the \(L_3,L_4,L_5\) libration points are retained even in the case of the lowest-order models.
scientific article; zbMATH DE number 1442270