CL_man_lambert

Description

• This function solves Lambert's problem in the case the transfer consists in less than one revolution.

  It Computes the velocity vectors vel1 and vel2, given the position vectors pos1 and pos2, the time of flight delta_t, and the direction of motion direction.

Parameters

pos1 :

Initial position vector [m] (3xN or 3x1)

pos2 :

Final position vector [m] (3xN or 3x1)

delta_t :

Time of flight from pos1 to pos2 [s] (1xN or 1x1)

direction :

(string, optional) 'pro' if the transfer orbit is prograde, 'retro' if the transfer orbit is retrograde (default is 'pro')

mu :

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

vel1 :

Initial velocity vector [m/s] (3xN)

vel2 :

Final velocity vector [m/s] (3xN)

Authors

• CNES - DCT/SB

Bibliography

• 1) Orbital Mechanics for Engineering Students, H.D. Curtis, Section 5.3 and Appendix D.11 (algorithm 5.2)

• 2) Modern astrodynamics Fundamentals and perturbation methods, V Bond and M Allman, Chapter 6.2

Examples

dt = 1000; // seconds kep1 = [7000.e3; 0.1; 1; 0; 0; 0]; kep2 = CL_ex_kepler(0, kep1, dt/86400); [pos1, vel1] = CL_oe_kep2car(kep1); [pos2, vel2] = CL_oe_kep2car(kep2); [vel1b, vel2b] = CL_man_lambert(pos1, pos2, dt); CL_norm(vel1-vel1b) + CL_norm(vel2-vel2b)