Name
CL_fr_lvlhMat — Local orbital frame (LVLH) definition in an inertial frame
Calling Sequence
[M] = CL_fr_lvlhMat(pos,vel)
Description
-
Given satellite's position and velocity vectors in a geocentric inertial frame,
this function computes the frame transfer matrix from the inertial frame to the local orbital frame LVLH.
- The LVLH local frame is defined as follows:
origin: center of gravity of the target
x: a unit vector that completes the direct orthogonal trihedral (if the orbit is circular, x coincides with the velocity vector)
z: a unit vector directed towards the planet center (opposite to the position vector)
y: a unit vector in the opposite direction of the angular momemtum

- Rows of matrix M are the following : M(1,:) = x, M(2,:) = y and M(3,:) = z
- To convert vectors from and to LVLH local frame, you can use one of the examples
- Last update : 31/10/2007
Parameters
- pos:
satellite's cartesien position in a geocentric inertiel frame [m] (3xN)
- vel:
satellite's cartesien velocity in a geocentric inertiel frame [m/s] (3xN)
- M :
frame transfer matrix from an inertial frame to the LVLH local frame (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
Examples
// Inertial to LVLH :
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_lvlhMat(pos_car,vel_car)
pos_lvlh = M*pos_car;
// LVLH to inertial :
pos_car = M'*pos_lvlh;