Effect of continuous low thrust on the Keplerian orbital elements (elliptical orbits)
[result] = CL_man_lowThrustApsKep(kep, acc, acc_frame, alpha, apsis, res [[, opts, mu]])
Computes the effect of a continuous low thrust maneuver on the Keplerian orbital elements.
The thrust acceleration is supposed to be zero everywhere except in an orbit portion centered on the periapsis or the apoapsis. The interval in true anomaly where the acceleration is not zero is:
- if apsis = "per" (periapsis): [ -alpha, +alpha ],
- if apsis = "apo" (apoapsis): [ pi - alpha, pi + alpha ].
The components of the thrust acceleration are given in a frame that can be: "qsw", "tnw" or "aps". "aps" is defined by: x axis from center of central body to periapsis and z axis towards the orbit's angular momentum.
The result of the computation is indicated by res:
- "dkepdt" : Orbital elements average time derivatives
- "dkep" : Increments on the orbital elements
The average time derivatives are by definition the increments on the orbital elements divided by one orbital period.
The argument opts is a structure that defines computation options:
- integr_meth: "int" (default) or "sq". "sq" means that some internal calculations are approximated (integrals computed by squaring), but are also faster.
Notes:
- Most of the formulas used come from Pollard's paper (see reference). Some results have been added: derivatives for the mean anomaly, or for the case the acceleration is parallel to the radius vector.
- The results are representative only if the thust acceleration is small enough.
- %nan is returned if the result is undefined or not yet coded. That's in particular the case if acc_frame is "tnw" and the "n" component is not 0.
Keplerian orbital elements [m, rad]. (6xN or 6x1)
Thust acceleration (in cartesian coordinates) in the specified frame [m/s^2]. (3xN or 3x1)
(string) Frame in which the acceleration is defined : "qsw", "tnw" or "aps". (1x1)
Angle (true anomaly) defining the thrust arc [rad]. (1xN or 1x1)
(string) Center of thrust arc : "per" or "apo". (1xN or 1x1)
(string) Computed result: "dkepdt" or "dkep". (1x1)
(structure, optional) Computation options (see above). Default: empty structure.
(optional) Gravitational constant. [m^3/s^2]. Default value is %CL_mu
Orbital elements time derivatives [m/s, rad/s] or increments [m, rad]. (6xN)
CNES - DCT/SB
Simplified Analysis of Low-Thrust Orbital Maneuvers, J. E. Pollard, The Aerospace Corporation, 15 August 2000.