$LastChangedDate: 27-Juil-2011 $

# CL_3b_lissajous

Lissajous orbit

## Calling Sequence

       [orb,omega,nu] = CL_3b_lissajous(env,Ax,phix,Az,phiz,epsilon,t_orb)

## Description

- Computes a Lissajous 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)

Ax:

  Amplitude in x (adimensional: use env.D, see CL_3b_environment)

phix:

  Phase in x [rad]

Az:

  Amplitude in z (adimensional: use env.D, see CL_3b_environment)

phiz:

  Phase in z [rad]

epsilon:

  Degree of accuracy

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]

omega:

  Lissajous orbit pulsation

nu:

  nu

## 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_halo

- CL_3b_lissajous

- CL_3b_manifolds

## Authors

- CNES - DCT/SB

## Examples

    env = CL_3b_environment('S-EM','l2');
    Ax = -30e6/env.D;
    phix = 0;
    Az = 100e6/env.D;
    phiz = 0;
    date_init = 0;
    epsilon=1e-10
    t_orb = linspace(0,4,100)*365.25*24*3600*env.OMEGA//4 years;
    orb = CL_3b_lissajous(env,Ax,phix,Az,phiz,epsilon,t_orb);
    plot(orb(1,:),orb(2,:),'g')
    f1 = scf();
    subplot(222); plot(orb(1,:),orb(3,:),'r'); xtitle('','X','Z'); plot2d(env.gl,0,-10);
    subplot(221);xgrid(); plot(orb(2,:),orb(3,:),'r'); xtitle('','Y','Z'); plot2d(0,0,-10);

    subplot(224); xgrid();plot(orb(1,:),orb(2,:),'r'); xtitle('','X','Y');plot2d(env.gl,0,-10);

    subplot(223);xstring(0.5,0.5,'Lissajous'' orbit');