CL_op_gauss

Description

• Computes Gauss equations for a given type of orbital elements, in the "qsw" or "tnw" frame.

  The function returns M and N such that d(oe)/dt = M*acc + N, where acc = acceleration with components in "qsw", "tnw" or "inertial" frame.

  The "inertial frame" option is only present for convenience (and is less efficient).

  Available types of orbital elements are: "kep", "cir", "cireq" and "equin".

  See Orbital elements for the definition of orbital elements

  Notes:

  - For orbital elements that have singularities (e.g Keplerian orbital elements with an eccentricity of zero) the parameters that cannot be computed are set to %nan.

Parameters

type_oe:

(string) Type of input orbital elements ("kep", "cir", "cireq", "equin" or "car") (1x1)

oe:

Input orbital elements (6xN)

frame:

(string) Coordinates frame for acceleration : "qsw", "tnw" or "inertial". (1x1)

mu:

(optional) Gravitational constant [m^3/s^2] (default value is %CL_mu)

M:

Effects of acceleration on orbital elements (6x3xN)

N:

Mean motion (6xN)

Authors

• CNES - DCT/SB

Bibliography

• 1) Les Equations du Mouvement Orbital Perturbe - Cours de l'Ecole GRGS 2002 - Pierre Exertier, Florent Deleflie

See also

• CL_oe_convert

Examples

// Keplerian orbital elements kep = [7000.e3;0.01;1.8;0.1;0.2;0.3]; [M,N] = CL_op_gauss("kep",kep,"qsw"); // d(kep)/dt due to some acceleration: acc = [1e-3 ; 1e-4; -2e-3]; // in qsw frame dkepdt = M*acc + N; // Same orbit, circular orbital elements [cir, dcirdkep] = CL_oe_kep2cir(kep); [M2,N2] = CL_op_gauss("cir",cir,"qsw"); // Check consistency using jacobian: M2 - dcirdkep*M // --> zero