Derivatives of eccentricity vector (ex, ey) with respect to time
[exdot, eydot] = CL_op_frozenOrbitDerCir(sma, ex, ey, inc [[, er, mu, j1jn]])
Computes the time derivatives of the eccentricity vector components resulting from the gravitational effects due to J2 and J3.
The eccentricity vector components are defined by: ex = e * cos(pom) and ey = sin(pom), where ecc is the eccentricity, and pom the argument of the periapsis.
The time derivatives are undefined (%nan) if the orbit is equatorial (inc = 0 or pi).
The formulas are equivalent to the ones presented below (see CL_op_frozenOrbitDer), except that they are valid even if eccentricity is 0:
Semi-major axis. [m] (1x1 or 1xN)
Eccentricity vector "x" component. [-] (1x1 or 1xN)
Eccentricity vector "y" component. [-] (1x1 or 1xN)
Inclination. [rad] (1x1 or 1xN)
(optional) Equatorial radius. Default: %CL_eqRad. [m] (1x1)
(optional) Gravitational constant. Default: %CL_mu. [m^3/s^2] (1x1)
(optional) Vector of zonal coefficients J1 to Jn, troncated to J3. Default: %CL_j1jn(1:3)). [-] (1xNz)
Time derivative of ex. [-/s] (1xN)
Time derivative of ey. [-/s] (1xN)
CNES - DCT/SB
1) "Frozen orbits in the J2+J3 problem", Krystyna Kiedron and Richard Cook, AAS 91-426.
sma = 7000.e3; ex = 1.e-4; ey = 1.2e-3; inc = CL_deg2rad(98.0); [exdot, eydot] = CL_op_frozenOrbitDerCir(sma, ex, ey, inc); // Check using CL_op_frozenOrbitDer ecc = sqrt(ex^2 + ey^2); pom = atan(ey, ex); // Derivatives of ecc and pom: [deccdt, dpomdt] = CL_op_frozenOrbitDer(sma, ecc, inc, pom); exdot2 = deccdt * cos(pom) - ecc * sin(pom) * dpomdt; eydot2 = deccdt * sin(pom) + ecc * cos(pom) * dpomdt; exdot - exdot2 // => 0 eydot - eydot2 // => 0 | ![]() | ![]() |