Name

CL_3b_manifolds — Manifolds (divergent and convergent) from Halo and Lissajous

Calling Sequence

   manifolds = CL_3b_lissajous_manifold(env,lissajous_orb,epsilon,tint,pars)
   [manifold1,...,manifoldN] = CL_3b_lissajous_manifold(env,orb,epsilon,tint,pars)
   
   

Description

  • Computes manifolds around the Lagrangian point defined in env.Lpoint (variable env can be obtained as output of function CL_3b_environment).

    This function accepts diferent number of outputs. Parameter pars is a string vector used to specifiy which outputs are computed. 'div' calculates divergent manifold using epsilon value while '-div' computes also divergent manifold but using -epsilon. In the same way, you can use 'conv' et '-conv' to compute convergent manifolds.

    Outputs will be in the same order as in pars. If size of pars is NP and number of outputs demanded is NO, then: for NP==NO each output contains a manifold (matrix). For NO==1 and NP>1, single output is a list of manifolds (list of matrixs).

  • Last update : 21/1/2009

Parameters

env:

environment around a Lagrangian point. Tlist of type environment (see CL_3b_environment)

orb:

lissajous or halo orbit, matrix 7xN (see CL_3b_lissajous) [m,m/s,t]

epsilon:

epsilon In the literature it's said about 200 Km ~1e-9, but this method is accurate enough, we recommended 1e-5

periode:

in order to estimate the monodromy

tint:

integration time

pars:

vector of strings specifying manifolds to calculate. Possible values are 'div','-div','conv' or '-conv'.

manifolds:

matrix or list of matrixs

Bibliography

1 Introduction au Probleme a Trois Corps et Dynamique Linearisee autour des Points de Lagrange, G. Collange, Note Technique CCT Mecanique Orbitale num.7, CNES 2006

2 Estimation numerique des varietes stables et instables des orbites quasi-periodiques de Lissajous autour des Points d'Euler (Lagrange L1, L2, L3), R. Alacevich, CNES septembre 2006

3 Rapport de Stage: Exploration Numerique d'orbites Homoclines et Heteroclines autour de L1 et L2 dans le probleme restreint a trois corps, A. Martinez Maida, DCT/SB/MO 2007.0029301, CNES 4 septembre 2007

See also

CL_3b_environment, CL_3b_lissajous, CL_3b_halo

Authors

CNES - DCT/SB

Examples

// First, we must build an orbit
env = CL_3b_environment('S-EM','L2');
Az = 150e6/env.D;
sens = 0;
t=[0:0.01:0.99*%pi];
[orb,omega] = CL_3b_halo(env,Az,sens,t);
// Then the manifolds itself
epsilon=1e-5;
tint =.4*%pi;
[div_in,conv_in,conv_out,div_out] = CL_3b_manifolds(env,orb,omega,epsilon,tint,['div','conv','-conv','-div']);
[div] = CL_3b_manifolds(env,orb,omega,epsilon,tint,['div']);