CL_cw_lambert

Description

• Computes the initial and final velocities of a transfer knowing the initial and final positions.

  The reference frame used is the target's LVLH local frame (origin = target).

  The reference altitude alt is the altitude of the target = semi major axis of target's (circular) orbit minus equatorial radius.

  acc is the differential inertial acceleration (corresponding to a physical force) with components in the reference frame.

Parameters

p1 :

Initial (relative) position vector, components in reference frame [m] (3xN or 3x1)

p2 :

Final (relative) position vector, components in reference frame [m] (3xN or 3x1)

delta_t :

Transfer time [s] (1xN or 1x1)

alt:

Reference altitude (= altitude of target) [m] (1x1)

acc:

(optional) Differential acceleration, components in reference frame (m/s^2). Default is []. (3xN or 3x1 or [])

er:

(optional) Equatorial radius [m]. Default is %CL_eqRad

mu:

(optional) Gravitational constant [m^3/s^2]. Default value is %CL_mu

v1:

Initial (relative) velocity vector in reference frame [m/s] (3xN)

v2:

Final (relative) velocity vector in reference frame [m/s] (3xN)

Authors

• CNES - DCT/SB

See also

• CL_cw_propagate

Bibliography

• 1) Mecanique spatiale, CNES - Cepadues 1995, Tome II, 16.3

• 2) Orbital Mechanics for engineering students, H D Curtis, Chapter 7 (section 7.5)

Examples

p1 = [10e3;10.e3;100.e3]; p2 = [-10e3;100.e3;20.e3]; delta_t = 1000; // sec alt = 450e3; [v1,v2] = CL_cw_lambert(p1,p2,delta_t,alt) // Check t1 = 0; t2 = delta_t/86400; // days [p2;v2] - CL_cw_propagate(t1,[p1;v1],t2,alt) // => 0