Name

CL_fr_tnwMat — Local orbital frame (t,n,w) definition in an inertial frame

Calling Sequence

   [M] = CL_fr_tnwMat(pos_car,vel_car)
   
   

Description

  • Given satellite's position and velocity vectors in an inertial frame, this function computes the frame transfer matrix from the inertial frame to the local orbital frame TNW.
  • The TNW local frame is defined as follows:

    origin: center of gravity of satellite

    t: unit vector in the direction of satellite's velocity

    w: unit vector of the kinetic moment of the osculating orbit

    n: unit vector chosen so TNW is a direct orthonormal frame

  • To convert a vector pos_car to pos_tnw, you can use the (hyper)matrix M : pos_tnw = M*pos_car

    To convert a vector pos_tnw to pos_car, you can use the (hyper)matrix M' : pos_car = M'*pos_tnw;

    For big hypermatrixes, it is faster to use the functions CL_fr_inertial2tnw and CL_fr_tnw2inertial

  • Last update : 07/11/2007

Parameters

pos_car:

satellite's cartesien position in a geocentric inertiel frame [m] (3xN)

vel_car:

satellite's cartesien velocity in a geocentric inertiel frame [m/s] (3xN)

M :

frame transfer matrix from an inertial frame to the TNW local frame (3x3xN)

Bibliography

1 Mecanique spatiale, CNES - Cepadues 1995, Tome I, section 10.2.2.3 (Definition du Repere orbital local)

2 CNES - MSLIB FORTRAN 90, Volume O (mo_def_tnw)

Authors

CNES - DCT/SB

See also

CL_fr_qsw2inertial, CL_fr_inertial2qsw, CL_fr_qswMat, CL_fr_inertial2tnw, CL_fr_tnw2inertial

Examples

// Inertial to TNW :
pos_car = [- 700700.,5.325E-11,6.718E-11;- 700700.,5.325E-11,6.718E-11]'
vel_car = [- 2.919E-12,- 14807.462,- 18682.367;- 2.919E-12,- 14807.462,- 18682.367]'
[M] = CL_fr_tnwMat(pos_car,vel_car)
pos_tnw = M*pos_car;

// TNW to inertial :
pos_car = M'*pos_tnw;