Coriolis loads

[janerikhy]

What

We should include Coriolis loads for models where we can't assume $\nu \approx 0$.

The following terms should be included in the EOM for those models: $C_{rb}(\nu)\nu$, $C_a(\nu_r)\nu_r$, and $M_a\dot{\nu}_c^b$.

How

One definition that could be used according to Fossen 2011:

If the system intertia matrix M has the property $$M = M^{\top} > 0$$ where $$M_{21} = M_{12}^{\top}$$.Then the Coriolis-centripetal matrix can be parameterized s.t. $C(\nu) = -C^{\top}_(\nu)$.

$$ C(\nu) = \left[\begin{array}{cc} 0_{3x3} & -S(M_{11}\nu_1 + M_{12}\nu_2 \\ -S(M_{11}\nu_1 + M_{12}\nu_2) & -S(M_{21}\nu_1 + M_{22}\nu_2) \end{array} \right] $$