Following the same central idea of Féjoz [9] [10] [8], we study the planar averaged 3-body problem without making use of series developments, as is usual, but instead we perform a global geometric analysis: the space of the orbits for a fixed energy is reduced under the rotational symmetry to a 2-dimensional symplectic manifold, where the motion is described by the level curves of the reduced Hamiltonian. The number and location of the critical points are investigated both analytically and numerically, confirming a conjecture of Féjoz.
Global study of 2D secular 3-body problem / Bruno Cordani. - In: REGULAR & CHAOTIC DYNAMICS. - ISSN 1560-3547. - 9:2(2004), pp. 113-128.
Global study of 2D secular 3-body problem
Bruno Cordani
2004
Abstract
Following the same central idea of Féjoz [9] [10] [8], we study the planar averaged 3-body problem without making use of series developments, as is usual, but instead we perform a global geometric analysis: the space of the orbits for a fixed energy is reduced under the rotational symmetry to a 2-dimensional symplectic manifold, where the motion is described by the level curves of the reduced Hamiltonian. The number and location of the critical points are investigated both analytically and numerically, confirming a conjecture of Féjoz.Pubblicazioni consigliate
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