Dynamics in the center manifold of the collinear points of the restricted three body problem

Details Dynamics in the center manifold of the collinear points of the restricted three body problem Dynamics in the center manifold of the collinear points of the restricted three body problem

Jul 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phyd..132..189j&link_type=abstract

Physica D: Nonlinear Phenomena, Volume 132, Issue 1-2, p. 189-213.

Physics

20

Center Manifolds, Normally Hyperbolic Manifolds, Lower Dimensional Tori, Lissajous Orbits, Halo Orbits

Scientific paper

This paper focuses on the dynamics near the collinear equilibrium points L1,2,3 of the spatial Restricted Three Body Problem (RTBP). It is well known that the linear behavior of these three points is of the type centerxcenterxsaddle. To obtain an accurate description of the dynamics in an extended neighborhood 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 so-called reduction to the center manifold. The study of the dynamics of this reduced Hamiltonian (now with only two degrees of freedom) gives a qualitative description of the phase space near the equilibrium point. Finally, a Lindstedt-Poincaré procedure is applied to explicitly compute the invariant tori contained in the center manifold. These tori are obtained as the Fourier series of the corresponding solutions, the frequencies being 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.

Affiliated with

Also associated with

No associations

Rating

Dynamics in the center manifold of the collinear points of the restricted three body problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamics in the center manifold of the collinear points of the restricted three body problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics in the center manifold of the collinear points of the restricted three body problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1577086