List of top Naval Architecture and Ocean Engineering Questions on Manoeuvring asked in GATE NM

The sway-yaw coupled maneuvering equation of motion for a ship is
\[ \begin{bmatrix} M - Y_{\dot{v}} & -Y_{\dot{r}} \\ -N_{\dot{v}} & I_z - N_{\dot{r}} \end{bmatrix} \begin{bmatrix} \dot{v} \\ \dot{r} \end{bmatrix} = \begin{bmatrix} Y_v & Y_r \\ N_v & N_r \end{bmatrix} \begin{bmatrix} v \\ r \end{bmatrix} + \begin{bmatrix} Y_{\delta} \\ N_{\delta} \end{bmatrix} \delta_R \]For a control-fixed straight-line stability, the eigenvalues of the function should be ______.

During a captive maneuvering model test of a ship with a rudder, which ONE or MORE of the following coefficients can be calculated using an oblique towing test (straight line test with a drift angle)?

A ship is undergoing a steady starboard turn. Assume that the total hydrodynamic forces \(Y\) including the rudder forces act at the centre of buoyancy \(B\).
If \(W\) is the weight of the ship, \(G\) is the centre of gravity and \(M\) is the transverse metacentre, then the magnitude of the heel angle \(\phi\) is given by ______.
Assume that \(\phi\) is small.