CL_rot_defFrameVec

Description

• This function defines a new frame based on 2 vectors.

  Considering two vectors u and v, the new frame basis vectors are such that:

  - n1 axis: aligned with u (and with same direction)

  - n2 axis: in the half-plane delimited by u and containing v

  where n1 and n2 are axis numbers: 1=>x-axis, 2=>y-axis, 3=>z-axis.

• If u and v are (nearly) aligned or if n1 and n2 are identical, the basis vectors are such that:

  - n1 axis: aligned with u (and same direction)

  - other axes: perpendicular to n1 axis (arbitrary directions).

• The outputs are:

  - M: Transformation matrix from the (implicit) reference frame to the new frame defined by u and v,

  - q: Quaternion of the rotation that transforms the axes of the (implicit) reference frame into the axes of the new frame defined by u and v,

  - Inok: Row vector that contains the indices for which the new frame is not uniquely defined.

• Note:

  - CL_rot_defFrameVec(u,[],n1,[]) is equivalent to: CL_rot_defFrameVec(u,u,n1,n1).

Parameters

u:

First vector (3xN or 3x1)

v:

Second vector (3xN or 3x1)

n1:

First axis number (axis colinear with u). Possibles values are: 1, 2 or 3 (1x1)

n2:

Second axis number (axis in the (u,v) plane). Possibles values are: 1, 2, 3 (1x1)

res:

(optional, string) Type of result: 'm': frame transformation matrix, q: rotation quaternion. Default is 'm'

meth:

(optional, string) Method used: 'm': Method based on matrices (faster), 'q': method based on quaternions (result consistent with CL_rot_defRotVec). Default is 'm'

M/q:

Frame transformation matrix (3x3xN) or rotation quaternion (dim N)

Inok:

Indices for which the new frame is not uniquely defined.

Authors

• CNES - DCT/SB

See also

• CL_rot_defRotVec

Examples

CL_rot_defFrameVec([1;0;0], [1;1;0], 1, 2) // => identity // Computes local orbital frame: kep = [7000.e3; 0.01; %pi/3 ; 0 ; 0; 0]; // orbital elements [r,v] = CL_oe_kep2car(kep); // position and velocity M = CL_rot_defFrameVec(r, v, 1, 2) // => "qsw" local frame q = CL_rot_defFrameVec(-r, v, 3, 1, res='q') //=> "lvlh" local frame