Generalized Hill's problem: Some cases of complete integrability
Tóm tắt
In this paper, we are investigating cases of integrability in the planar Hill's problem. The external potential U
extis supposed to be time independent in a given uniformly rotating frame. Cases of integrability of the relative motion of two interacting particles in the vicinity of an equilibrium solution of U
extare found. In all these cases, the form of the second integral is explicitly given, the first being the Jacobian one. Cases in which the interacting potential U between the two particles is of newtonian type are particularized.
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