$LastChangedDate: 27-Juil-2011 $

# CL_fr_tnwMat

Inertial frame to TNW local orbital frame transformation matrix

## Calling Sequence

       [M] = CL_fr_tnwMat(pos_car,vel_car)

## Description

- Computes the frame transformation matrix M from the inertial reference frame to the TNW local orbital frame.

  The inertial frame is implicitly the frame relative to which the satellite's position and velocity are defined. The TNW local frame is built using these position and velocity vectors.

  By convention, M multiplied by coordinates relative to the inertial frame yields coordinates relative to the TNW frame.

- See Local Frames for more details on the definition of local frames.

## Parameters

pos_car:

  satellite's position relative to the inertial frame [m] (3xN)

vel_car:

  satellite's velocity relative to the inertial frame [m/s] (3xN)

M :

  inertial frame to TNW local frame transformation matrix (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 = [[3500.e3;2500.e3;5800.e3] , [4500.e3;2100.e3;6800.e3]];
    vel_car = [[1.e3;3.e3;7.e3] , [2.e3;3.e3;6.e3]];
    [M] = CL_fr_tnwMat(pos_car,vel_car)
    pos_tnw = M*pos_car;

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