$LastChangedDate: 27-Juil-2011 $

# CL_fr_lvlhMat

Inertial frame to LVLH local orbital frame transformation matrix

## Calling Sequence

       [M] = CL_fr_lvlhMat(pos_car,vel_car)

## Description

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

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

  By convention, multiplying M by coordinates relative to the inertial frame yields coordinates relative to the LVLH frame.

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

## Parameters

pos_car:

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

vel_car:

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

M :

  inertial frame to LVLH local frame transformation matrix (3x3xN)

## Bibliography

- 1) Mecanique spatiale, CNES - Cepadues 1995, Tome II, section 16.3.2.1

- 2) Orbital Mechanics for engineering students, H D Curtis, Chapter 7

## Authors

- CNES - DCT/SB

## See also

- CL_fr_qswMat

- CL_fr_tnwMat

## Examples

    // Inertial to LVLH :
    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_lvlhMat(pos_car,vel_car)
    pos_lvlh = M*pos_car;

    // LVLH to inertial :
    pos_car = M'*pos_lvlh;