$LastChangedDate: 27-Juil-2011 $

# CL_ex_lyddane

Lyddane orbit propagation analytical model

## Calling Sequence

       [mean_kep_t2,osc_kep_t2] = CL_ex_lyddane(t1,mean_kep_t1,t2 [,er,mu,zonals])

## Description

- Computes the mean orbital elements mean_kep_t2 and the osculating elements osc_kep_t2 at time t2 given the mean elements mean_kep_t1 at time t1.

  Zonals coefficients up to J5 are taken into account.

- The function works in the following cases:

  - 1 initial time and 1 set of initial orbital elements, and N final times.

  - N (or 1) initial times and N sets of initial orbital elements, and N (or 1) final times.

- The orbital elements are the following:

- Warnings :

  - This function does not work for inclinations close to the critical inclinations (63.43494882 deg and 116.5650512 deg)

  - This function does not work for eccentricities higher than 0.9

## Parameters

t1:

  Initial time [days] (1xN ot 1x1)

mean_kep_t1:

  Mean Keplerian elements at time t1 [sma;ecc;inc;pom;raan;anm] (6xN or 6x1).

t2:

  Final time [days] (1xN or 1x1).

er:

  (optional) Equatorial radius [m] (default is %CL_eqRad)

mu:

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

zonals:

  (optional) Vector of zonal coefficients J1 to Jn (troncated to J5) to be used (default is %CL_j1jn(1:5)) (Nz x 1)

mean_kep_t2:

  Mean Keplerian elements at t2 [sma;ecc;inc;pom;raan;anm] (6xN)

osc_kep_t2:

  Osculating Keplerian elements at t2 [sma;ecc;inc;pom;raan;anm] (6xN)

## Authors

- CNES - DCT/SB

## Bibliography

- 1) CNES - MSLIB FORTRAN 90, Volume E (me_lyddane)

## See also

- CL_ex_meanLyddane

- CL_ex_lyddaneMan

## Examples

    t1 = 12584 ;
    mean_kep_t1 = [7078e3;7.9e-3;CL_deg2rad([97.2; 89; 125; 0])] ;
    t2 = 12587:0.2:12588 ;
    [mean_kep_t2,osc_kep_t2] = CL_ex_lyddane(t1,mean_kep_t1,t2)