 98431 Jorba A., Masdemont J.
 Dynamics in the centre manifold of the collinear
points of the Restricted Three Body Problem
(1286K, PostScript (gzipped and uuencoded))
Jun 11, 98

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. This paper focuses on the dynamics near the collinear equilibrium
points $L_{1,2,3}$ of the spatial Restricted Three Body Problem. It is
well known that the linear behaviour of these three points is of the
type center$\times$center$\times$saddle. To obtain an accurate
description of the dynamics in an extended neighbourhood of those
points, two different (but complementary) strategies are used.
First, the Hamiltonian of the problem is expanded in power series
around the equilibrium point. Then, a partial normal form scheme is
applied in order to uncouple (up to high order) the hyperbolic
directions from the elliptic ones. Skipping the remainder we have that
the (truncated) Hamiltonian has an invariant manifold tangent to the
central directions of the linear part. The restriction of the
Hamiltonian to this manifold is the socalled reduction to the centre
manifold. The study of the dynamics of this reduced Hamiltonian (now
with only 2 degrees of freedom) gives a qualitative description of the
phase space near the equilibrium point.
Finally, a LindstedtPoincar\'e procedure is applied to explicitly
compute the invariant tori contained in the centre manifold. These
tori are obtained as the Fourier series of the corresponding
solutions, being the frequencies a power expansion of some parameters
(amplitudes). This allows for an accurate quantitative description of
these regions. In particular, the well known Halo orbits are obtained.
 Files:
98431.uu