$LastChangedDate: 27-Juil-2011 $

# CL_man_lambert

Lambert's problem

## Calling Sequence

       [v1,v2] = CL_man_lambert(pos1,pos2,delta_t,direction [,mu])

## Description

- Computes the velocity vectors v1 and v2, given the position vectors r1 and r2, the time of flight delta_t, and the direction of motion direction.

## Parameters

pos1 :

  Initial position vector [m] (3xN)

pos2 :

  Final position vector [m] (3xN)

delta_t :

  Time of flight from r1 to r2 [s] (1xN or 1x1)

direction :

  (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]

v1 :

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

v2 :

  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

## See also

- CL_stumpS

- CL_stumpC

## Examples

    r1 = [5000.e3 ; 10000.e3 ;2100.e3];
    r2 = [-14600.e3 ; 2500.e3 ;7000.e3];
    dt = 3600; //one hour
    // direction = 'pro' by default
    [v1, v2] = CL_man_lambert([r1 r1],[r2 r2],[dt dt]);