## 4 Methodology
### Response and Track Prioritization
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \(\mathbf{P}\) & \(\mathbf{V}\) & \(\mathbf{\dot{\phi}}\) & \(\mathbf{\dot{\theta}}\) & \(\mathbf{\dot{z}}\) & \(\mathbf{\dot{z_{1}}}\) & \(\mathbf{\dot{z_{3}}}\) & \(\mathbf{\dot{y_{1}}}\) & \(\mathbf{\dot{y_{3}}}\) \\ \hline \multirow{2}{*}{\(I_{xx}\)} & L & \(\varnothing\) & \(-22\) & \(1\) & \(-12\) & \(3\) & \(-3\) & \(2\) \\  & H & \(-4\) & \(-19\) & \(\varnothing\) & \(-9\) & \(\varnothing\) & \(\varnothing\) & \(\varnothing\) \\  & L & \(-18\) & \(\varnothing\) & \(\varnothing\) & \(\varnothing\) & \(-2\) & \(\varnothing\) & \(-3\) \\ \multirow{2}{*}{\(I_{yy}\)} & H & \(-25\) & \(\varnothing\) & \(\varnothing\) & \(1\) & \(\varnothing\) & \(\varnothing\) & \(\varnothing\) \\  & L & \(\varnothing\) & \(-3\) & \(-13\) & \(-6\) & \(-15\) & \(\varnothing\) & \(\varnothing\) \\ \multirow{2}{*}{\(M_{s}\)} & H & \(9\) & \(-2\) & \(-13\) & \(-6\) & \(-12\) & \(\varnothing\) & \(\varnothing\) \\  & L & \(-6\) & \(18\) & \(2\) & \(22\) & \(15\) & \(7\) & \(5\) \\ \multirow{2}{*}{\(l_{f}\)} & H & \(\varnothing\) & \(20\) & \(\varnothing\) & \(19\) & \(12\) & \(-3\) & \(3\) \\  & L & \(3\) & \(3\) & \(6\) & \(5\) & \(6\) & \(-3\) & \(\varnothing\) \\ \multirow{2}{*}{\(K_{f}\)} & H & \(1\) & \(1\) & \(2\) & \(\varnothing\) & \(\varnothing\) & \(5\) & \(\varnothing\) \\  & L & \(-3\) & \(\varnothing\) & \(-2\) & \(\varnothing\) & \(\varnothing\) & \(3\) & \(-3\) \\ \multirow{2}{*}{\(K_{r}\)} & H & \(\varnothing\) & \(-4\) & \(1\) & \(\varnothing\) & \(\varnothing\) & \(\varnothing\) & \(3\) \\  & L & \(12\) & \(12\) & \(8\) & \(14\) & \(7\) & \(-4\) & \(-3\) \\ \multirow{2}{*}{\(C_{f}\)} & H & \(7\) & \(4\) & \(2\) & \(6\) & \(1\) & \(10\) & \(\varnothing\) \\  & L & \(6\) & \(2\) & \(8\) & \(3\) & \(9\) & \(\varnothing\) & \(-6\) \\ \multirow{2}{*}{\(C_{r}\)} & H & \(\varnothing\) & \(2\) & \(\varnothing\) & \(\varnothing\) & \(4\) & \(\varnothing\) & \(-10\) \\ \multirow{2}{*}{\(M_{uf}\)} & L & \(7\) & \(2\) & \(6\) & \(8\) & \(8\) & \(-7\) & \(\varnothing\) \\  & H & \(9\) & \(-5\) & \(5\) & \(3\) & \(8\) & \(-11\) & \(\varnothing\) \\ \multirow{2}{*}{\(M_{ur}\)} & L & \(\varnothing\) & \(\varnothing\) & \(-2\) & \(\varnothing\) & \(\varnothing\) & \(\varnothing\) & \(-5\) \\ \multirow{2}{*}{\(K_{t}\)} & H & \(-4\) & \(\varnothing\) & \(-5\) & \(-3\) & \(-5\) & \(\varnothing\) & \(\varnothing\) \\  & L & \(3\) & \(10\) & \(3\) & \(6\) & \(8\) & \(11\) & \(10\) \\ \multirow{2}{*}{\(C_{t}\)} & H & \(17\) & \(19\) & \(15\) & \(15\) & \(12\) & \(20\) & \(19\) \\  & L & \(2\) & \(4\) & \(2\) & \(3\) & \(4\) & \(6\) & \(2\) \\ \multirow{2}{*}{\(M_{uf}\)} & H & \(-10\) & \(-7\) & \(-6\) & \(-3\) & \(-4\) & \(\varnothing\) & \(\varnothing\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter \(P\) response mapping for low- and high-speed tests for low-severity herringbone track. The effects of parameters on the amplitudes of roll and pitch rates and bounce, body and axle point acceleration responses is reported. Figure 8: (**a**) Kinematics of a rigid wheel going over a sinusoidal road. (**b**) The road displacement input acting on the wheel contact point P as seen at O. This particular road displacement input is for a vehicle running at a speed of 9 kmph on a low-severity herringbone track. interest. Table 5 is the average of the dependencies of each parameter on every response for all the tracks considered in Table 3.  
_Track Prioritization_: In the next step of the procedure, a response-to-track mapping matrix is constructed to identify the dominant effect of a particular response on a particular test track of interest. As an illustration of the rationale behind this, it is observed in the vehicle simulation performed on a low-severity herringbone track at low and high speeds that as the vehicle speed \(V\) is increased from low to high (\(\uparrow\)), the change in the response of interest is shown as a percentage increase or decrease as compared to its value at low speed.