CL_op_frozenOrbitDer

Description

• Computes the time derivatives of eccentricity and argument of periapsis resulting from the gravitational effects due to J2 and J3.

  The time derivative of the argument of periapsis is undefined (%nan) if the orbit is circular (ecc = 0) or equatorial (inc = 0 or pi).

  (See the formulas, where: R = equatorial radius, n = keplerian mean motion)

  

• Warning :

  - The input argument "zonals" is deprecated as of CelestLab v3.0.0. It has been replaced by "j1jn".

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)

j1jn:

(optional) Vector of zonal coefficients J1 to Jn, troncated to J3. Default is %CL_j1jn(1:3)). (1xNz)

deccdt:

Time derivative of eccentricity [s^-1] (1xN)

dpomdt:

Time 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 = [7000.e3, 73000.e3]; inc = CL_deg2rad([51.6, 91.6]); [ecc,pom] = CL_op_frozenOrbit(sma,inc); ecc = 0.999*ecc; pom = 0.999*pom; [deccdt,dpomdt] = CL_op_frozenOrbitDer(sma,ecc,inc,pom)