Hmm, my series is a result of some facts:
Omega is a skew-symmetric matrix
C is an orthogonal matrix where you have take the transpose of the Peano-Baker series.
C itself is the final result. In attitude determination problem, the propagation of C itself and obtaining the C at any instant of...
The last solution that I wrote is solution to
\dot{\mathbf{C}}_b^i = \mathbf{C}_b^i \mathbf{\Omega}_{ib}^b
starting from the Peano-Baker series itself.
And I think I should be able to expand the same thing out by using your formal solution which is no different...
@Kosovtov: Thanks, to be truthful I am not sure it's very helpful, but the furthest that I can go is to write
\mathbf{C}_b^n(t) = \mathbf{I} + \int_{t_0}^t \mathbf{\Omega}_{rb}^b(\sigma_1} d\sigma_1 + \int_{t_0}^t \left(\int_{t_0}^{\sigma_1} \mathbf{\Omega}_{rb}^b(\sigma_2} d\sigma_2...
My sub- and super-script is used to denote the frames which we are working on.
For all transformation matrix (or direction cosine matrix, here)
\mathbf{C}_a^b
denotes the rotation/transformation matrix from Frame a to b.
And for all angular velocity skew-symmetric matrix
\mathbf{\Omega}_{ab}^b...
Hi guys,
I am doing navigation mathematics and I met all kinds of references regarding how the attitude update equation should be solved. However, none of the references that I found makes any sense to me.
I wonder if someone could enlighten me with this math.
The attitude update equation for...