$LastChangedDate: 27-Juil-2011 $

# CL_3b_halo

Halo orbit

## Calling Sequence

       [orb,omegahalo] = CL_3b_halo(env,Az,direction,t_orb)

## Description

- Computes a halo orbit around a Lagrangian point.

- Notes:

  - Before using this function, it is needed to create an "environment" (env) for the chosen libration point and the chosen system (see CL_3b_environment).

## Parameters

env:

  Lagrangian point structure (See CL_3b_environment)

Az:

  First order of amplitude along Z axis (adimensional: use env.D) (See CL_3b_environment)

direction:

  Halo direction, 0 for North orientation or 1 for South orientation

t_orb:

  Times of the final orbit (adimensional: use env.OMEGA) (See CL_3b_environment))

orb:

  Stabilized trajectory: [x;y;z;vx;vy;vz] (6xN)

omegahalo:

  Halo orbit pulsation

## 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) Exploration numerique d'orbites homoclines et heteroclines autour de L1 et L2 dans le probleme restreint a trois corps, rapport de stage, A. Martinez Maida, DCT/SB/MO 2007.0029301, CNES septembre 2007

## See also

- CL_3b_environment

- CL_3b_lissajous

- CL_3b_manifolds

## Authors

- CNES - DCT/SB

## Examples

    env = CL_3b_environment('S-EM','l2');
    Az = 150e6/env.D;
    direction = 0;
    t_orb=linspace(0,180,50)*24*3600*env.OMEGA; //180 days
    [orb,omega] = CL_3b_halo(env,Az,direction,t_orb);
    plot(orb(1,:),orb(2,:),'g');