CL_3b_manifolds — Manifolds (divergent and convergent) from Halo and Lissajous
manifolds = CL_3b_lissajous_manifold(env,lissajous_orb,epsilon,tint,pars) [manifold1,...,manifoldN] = CL_3b_lissajous_manifold(env,orb,epsilon,tint,pars)
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).
environment around a Lagrangian point. Tlist of type environment (see CL_3b_environment)
lissajous or halo orbit, matrix 7xN (see CL_3b_lissajous) [m,m/s,t]
epsilon In the literature it's said about 200 Km ~1e-9, but this method is accurate enough, we recommended 1e-5
in order to estimate the monodromy
integration time
vector of strings specifying manifolds to calculate. Possible values are 'div','-div','conv' or '-conv'.
matrix or list of matrixs
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
// 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']);