Inverting rotations

A rotation represented by direction cosine matrix or quaternion can be inverted using the function:

inv_rotation(R)

in which R must be a DCM or a Quaternion.

Note

If R is a DCM, then the transpose matrix will be returned. Hence, the user must ensure that the input matrix is ortho-normalized. Otherwise, the result will not be the inverse matrix of the input.

If R is a Quaternion, then the conjugate quaternion will be returned. Hence, the user must ensure that the input quaternion is normalized (have unit norm). Otherwise, the result will not be the inverse quaternion of the input.

These behaviors were selected to alleviate the computational burden.

julia> D1 = angle_to_dcm(0.5, 0.5, 0.5, :XYZ)DCM{Float64}:
  0.770151   0.622447  -0.139381
 -0.420735   0.659956   0.622447
  0.479426  -0.420735   0.770151
julia> D2 = inv_rotation(D1)DCM{Float64}:
  0.770151  -0.420735   0.479426
  0.622447   0.659956  -0.420735
 -0.139381   0.622447   0.770151
julia> D2 * D1DCM{Float64}:
  1.0          3.41413e-17  -1.73278e-17
  3.41413e-17  1.0           1.97327e-17
 -1.73278e-17  1.97327e-17   1.0
julia> q1 = angle_to_quat(0.5, 0.5, 0.5, :XYZ)Quaternion{Float64}:
  + 0.894463 + 0.291567⋅i + 0.172955⋅j + 0.291567⋅k
julia> q2 = inv_rotation(q1)Quaternion{Float64}:
  + 0.894463 - 0.291567⋅i - 0.172955⋅j - 0.291567⋅k
julia> q2 * q1Quaternion{Float64}:
  + 1.0 + 0.0⋅i - 1.38778e-17⋅j + 0.0⋅k