CL_man_lambert2

Description

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

  Set direction to 'pro' for a prograde orbit. That is a counter-clockwise rotation around the Z axis. (this is the prograde direction for the solar system)

  Set direction to 'retro' for a retrograde orbit. That is a clockwise rotation around the Z axis. (this is the retrograde direction for the solar system)

  The number of revolutions m can optionaly be set to a value superior to 0, and in that case there are two solutions which can be selected using leftbranch

  

Parameters

pos1 :

Initial position vector [m] (3xN)

pos2 :

Final position vector [m] (3xN)

tf :

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

direction :

(optional) 'pro' for prograde, 'retro' for retrograde (default is 'pro') (1x1)

m :

(optional) number of revolution (default is 0) (1x1)

leftbranch :

(optional) (boolean) when m > 0, chooses between left branch or right branch (default is %f) (1x1)

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) Izzo, D. ESA Advanced Concepts team. Code used available in MGA.M, on http://www.esa.int/gsp/ACT/inf/op/globopt.htm. Last retreived Nov, 2009.

See also

Examples

dt = 1000; // seconds kep1 = [7000.e3; 0.1; 1; 0; 0; 0]; kep2 = CL_ex_kepler(0, kep1, dt/86400); [p1, v1] = CL_oe_kep2car(kep1); [p2, v2] = CL_oe_kep2car(kep2); [v1b, v2b] = CL_man_lambert2(p1, p2, dt); CL_norm(v1-v1b) + CL_norm(v2-v2b)