1 Correction to: Journal of Marine Science and Technology https://doi.org/10.1007/s00773-018-0546-2

In the original publication of the article Eqs. (1) and (10) are incorrectly published. The correct equations are provided in this correction article.

$$ \left\{ \begin{gathered} m_{k} (\mathop {u_{k} }\limits^{.} + q_{k} w_{k} - v_{k} r_{k} ) = X_{{Hk}} \hfill \\ \;\; + X_{{Pk}} + X_{{Rk}} + X_{{Tk}} \hfill \\ m_{k} (\mathop {v_{k} }\limits^{.} + u_{k} r_{k} - p_{k} w_{k} ) = Y_{{Hk}} \hfill \\ \;\; + Y_{{Pk}} + Y_{{Rk}} + Y_{{Tk}} \hfill \\ m_{k} (\mathop {w_{k} }\limits^{.} + p_{k} v_{k} - q_{k} u_{k} ) = Z_{{Hk}} \hfill \\ \;\; + Z_{{Pk}} + Z_{{Rk}} + Z_{{Tk}} \hfill \\ I_{{xk}} \mathop {p_{k} }\limits^{.} + (I_{{zk}} - I_{{yk}} )q_{k} r_{k} = K_{{Hk}} \hfill \\ \;\; + K_{{Pk}} + K_{{Rk}} + K_{{Tk}} \hfill \\ I_{{yk}} \mathop {q_{k} }\limits^{.} + (I_{{xk}} - I_{{zk}} )p_{k} r_{k} = M_{{Hk}} \hfill \\ \;\; + M_{{Pk}} + M_{{Rk}} + M_{{Tk}} \hfill \\ I_{{zk}} \mathop {r_{k} }\limits^{.} + (I_{{yk}} - I_{{xk}} )p_{k} q_{k} = N_{{Hk}} \hfill \\ \;\; + N_{{Pk}} + N_{{Rk}} + N_{{Tk}} \hfill \\ \end{gathered} \right. $$
(1)
$$ \left[ {\begin{array}{*{20}c} {{\text{d}}X/{\text{d}}s} \\ {{\text{d}}Y/{\text{d}}s} \\ {{\text{d}}Z/{\text{d}}s} \\ \end{array} } \right] = (1 + \varepsilon )T_{C}^{{ - 1}} \left[ {\begin{array}{*{20}c} 0 \\ 1 \\ 0 \\ \end{array} } \right], $$
(10)

In addition, the third sentence in the first paragraph of Sect. 2.1, "the added masses and inertia are represented by m and J with subscripts of x, y and z" should be cancelled.