$LastChangedDate: 27-Juil-2011 $

# CL_op_frozenOrbitDer

Derivatives of eccentricity and argument of periapsis with respect to time

## Calling Sequence

       [d_ecc_dt,d_pom_dt] = CL_op_frozenOrbitDer(sma,ecc,inc,pom, [er,mu,zonals])

## Description

- Computes the derivatives of eccentricity and argument of periapsis with respect to time that correspond to the gravitational effects due to J2 and J3.

## Parameters

sma:

  Semi-major axis [m] (1x1 or 1xN)

ecc:

  Eccentricity (1x1 or 1xN)

inc:

  Inclination [rad] (1x1 or 1xN)

pom:

  Argument of pariapsis [rad] (1x1 or 1xN)

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 J3. Default is %CL_j1jn(1:3)). (1xNz)

d_ecc_dt:

  Derivative of eccentricity [s^-1] (1xN)

d_pom_dt:

  Derivative of argument of periapsis [rad/s] (1xN)

## Authors

- CNES - DCT/SB

## Bibliography

- 1) "Frozen orbits in the J2+J3 problem", Krystyna Kiedron and Richard Cook, AAS 91-426.

## Examples

    sma = [%CL_eqRad+350.e3 %CL_eqRad+700.e3];
    inc = CL_deg2rad([51.6 91.6]);
    [ecc,pom] = CL_op_frozenOrbit(sma,inc);
    ecc = 0.999*ecc;
    pom = 0.999*pom;
    [d_ecc_dt,d_pom_dt] = CL_op_frozenOrbitDer(sma,ecc,inc,pom)