A Hopf variables view on the libration points dynamics. (English) Zbl 1375.70047
Summary: The dynamics about the libration points of the Hill problem is investigated analytically. In particular, the use of perturbation theory allows to reduce the problem to a one degree of freedom Hamiltonian depending on two dynamical parameters. The invariant manifolds structure of the Hill problem is then disclosed, yet accurate computations are limited to energy values close to that of the libration points.
MSC:
| 70F15 | Celestial mechanics |
Keywords:
libration points; Hill’s problem; center manifold; perturbation theory; elliptic oscillator; periodic orbits; Lissajous variables; Hopf variables; resonant normal formReferences:
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