$LastChangedDate: 27-Juil-2011 $

# CL_man_apsidesLine

Delta V required to change the line of apsides

## Calling Sequence

       [dv,anv] = CL_man_apsidesLine(ai,ei,pomi,pomf [,posman,mu])

## Description

- Computes the velocity increment needed to modify the line of apsides.

  The maneuver consists in making the orbit rotate in the orbit plane. Thus, only the argument of periapsis is changed; the semi major axis or the eccentricity are not.

  The output argument dv is the velocity increment expressed in spherical coordinates in the QSW local frame:

  dv = [lambda;phi;dv] (lambda: in-plane angle (pi = towards planet and pi/2 ~ along velocity), phi: out-of-plane angle, positive towards the angular momentum vector (the angular momentum vector is perpendicular to the orbit plane and oriented according to the right hand rule), dv: norm of delta-V).

  anv is the true anomaly at the position of maneuver.

  posman can be used to define where the maneuver takes place: 0->close to periapsis, 1->close to apoapsis, default is 0)

## Parameters

ai :

  Initial semi major axis [m] (1xN)

ei:

  Initial eccentricity (1xN)

pomi:

  Initial argument of periapsis [rad] (1xN)

pomi:

  Final argument of periapsis [rad] (1xN)

posman:

  (optional) Flag specifying the maneuver location (0->close to periapsis, 1->close to apoapsis, default is 0) (1xN)

mu :

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

dv :

  Delta-V in spherical coordinates in the QSW frame [lambda;phi;|dv|] [rad,rad,m/s] (3xN)

anv:

  True anomaly at the position of maneuver [rad] (1xN)

## Authors

- CNES - DCT/SB

## See also

- CL_man_biElliptic

- CL_man_hohmann

- CL_man_sma

- CL_man_hohmannG

- CL_man_inclination

## Examples

    ai = 7200.e3;
    ei = 0.1;
    pomi = CL_deg2rad(65);
    pomf = CL_deg2rad(85);
    [dv,anv] = CL_man_apsidesLine(ai,ei,pomi,pomf,1)
    // Check results :
    anm = CL_kp_v2M(ei,anv);
    kep = [ai ; ei ; %pi/2 ; pomi ; 0 ; anm];
    kep1 = CL_man_applyDv(kep,dv)