In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem / Lei, Hanlun; Xu, Bo; CIRCI, Christian. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 130:5(2018), pp. 1-34. [10.1007/s10569-018-9828-6]

### Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

#### Abstract

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.
##### Scheda breve Scheda completa
2018
equilibrium points; invariant manifolds; periodic orbits; polynomial expansions
01 Pubblicazione su rivista::01a Articolo in rivista
Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem / Lei, Hanlun; Xu, Bo; CIRCI, Christian. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 130:5(2018), pp. 1-34. [10.1007/s10569-018-9828-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1174824`