CL_3b_halo

Description

• Computes a halo orbit around a Lagrangian point.

  The approximate amplitude along the Z axis if given by Az.

  The motion around +X axis can specified by direction:

  - direction = "pro": prograde motion around +X axis

  - direction = "retro": retrograde motion around +X axis

  The orbit is such that the Y component at the initial time (t_orb = 0) is 0.

• 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).

  - For the definition of adimensional quantities, see CL_3b_environment.

Parameters

env:

(struct) Lagrangian point structure

Az:

Estimate of amplitude along the Z axis (adimensional)

direction:

(string) Motion direction around +X axis: "pro" = prograde, "retro" = retrograde

t_orb:

Time instants at which the orbit is computed (adimensional) (1xN)

orb:

Position and velocity [x;y;z;vx;vy;vz] defining the orbit (adimensional) (6xN)

omegahalo:

Orbit's angular rate (adimensional)

See also

• CL_3b_environment

• CL_3b_lissajous

Authors

• CNES - DCT/SB

Examples

env = CL_3b_environment("S-EM", "L2"); Az = 150.e6 / env.D; // adimensional direction = "pro"; t_orb = linspace(0,360*86400,100) * env.OMEGA; // 360 days -> adimensional [orb,omega] = CL_3b_halo(env,Az,direction,t_orb); // Plot orbit (normalized coordinates) scf(); param3d((orb(1,:)-env.gl), orb(2,:), orb(3,:)); xtitle("Orbit (3D), origin = Lagrange point");