Examples
// Reference orbital elements (circular type) cir = [7000.e3; 1.e-5; 1.e-3; 1; 2; 3]; // Normalized matrices M0 = CL_op_orbGapLofMat("cir", cir, "qsw", "f0") // order 0 M = CL_op_orbGapLofMat("cir", cir, "qsw") // reference |  |  |
Orbital elements to pos/vel in local frame (Jacobian)
M = CL_op_orbGapLofMat(type_oe, oe, loc_frame, meth [, motion, form, mu])
Computes the jacobian of the transformation from orbital elements to position and (inertial) velocity in the specified local orbital frame.
The jacobian matrix can be normalized (form = "n") or unnormalized (form = "un"). The normalized form corresponds to the transformation (for elliptical orbits only):
[dpos/sma; dvel/(n*sma)] = M * [dsma/sma; ...], with n = mean motion.
The available calculation methods are:
- c: The jacobian is computed numerically (no explicit formulas),
- f: The jacobian is given by explicit formulas (no approximation),
- f1: Same as "f", but the formulas are developped to order 1 in eccentricity,
- f0: Same as "f", but the formulas are developped to order 0 in eccentricity.
Notes:
- Methods f0, f1, f are only available for elliptical orbits.
- Methods f0 and f1 are only available for "kep" or "cir" orbital elements and "tnw" or "qsw" local frames.
- Relative motion is only available for "f0" methods.
See Local frames for more details on the definition of local frames.
See Orbital elements for more details on orbital elements.
(string) Type of orbital elements (1x1)
Reference orbital elements (6xN)
(string) Name of local orbital frame (1x1)
(string, optional) Method used: "f", "f1", "f0", "c". Default is "c"
(optional, string) "abs" = absolute motion, "rel" = relative motion. Default is "abs"
(optional) Matrix option: "n" = normalized, "un" = unnormalized. Default is "n"
(optional) Gravitational constant [m^3/s^2]. Default value is %CL_mu
Jacobian in normalized or unnormalized form (6x6xN)
CNES - DCT/SB
1) Casotto S, Position and velocity perturbation in the orbital frame in terms of classical elements perturbation, 1991.
// Reference orbital elements (circular type) cir = [7000.e3; 1.e-5; 1.e-3; 1; 2; 3]; // Normalized matrices M0 = CL_op_orbGapLofMat("cir", cir, "qsw", "f0") // order 0 M = CL_op_orbGapLofMat("cir", cir, "qsw") // reference | | |