## 2 Materials and Methods
### Mathematical Modeling
#### 2.1.1 Traditional Passive Suspension Model  
For the traditional suspension layout, the suspension system was modelled having the BlueStreamline BS19 car as a reference where each wheel is connected to the chassis with a linear helicoidal spring paired with a hydraulic damper, plus front and rear ARBs. Some modifications are made to [PERSON]'s model ([11] pp. 891-892) in order to accommodate the different front and rear track sizes of the BS19 as well as the inclusion of a rear ARB. The equations of motion are obtained using a Lagrange equation for small and linear vibration. We obtain the following equation of motion:  
\[ \begin{split}\mathrm{m\ddot{x}}+\Big{(}2\dot{x}-\dot{x}_{1}-\dot{x }_{2}-2a_{1}\dot{\theta}\Big{)}c_{\rm f}+\Big{(}2\dot{x}-\dot{x}_{3}-\dot{x}_{4 }+2a_{2}\dot{\theta}\Big{)}c_{\rm r}+(2x-x_{1}-x_{2}-2a_{1}\theta)k_{\rm f}\\ +(2x-x_{3}-x_{4}-2a_{2}\theta)k_{\rm r}=-F_{\rm aero-t}\end{split}  \tag{11}\]  
\[ \begin{split}\mathrm{I}_{\rm x}\dot{\theta}+\Big{(}2b_{1}\dot{ \theta}-\dot{x}_{1}+\dot{x}_{2}\Big{)}b_{1}c_{\rm f}+\Big{(}2b_{2}\dot{\theta }+b_{2}\dot{x}_{3}-b_{2}\dot{x}_{4}\Big{)}b_{2}c_{\rm r}+(2b_{1}\phi-x_{1}+x_{ 2})b_{1}k_{\rm f}\\ +(2b_{2}\phi+x_{3}-x_{4})b_{2}k_{\rm r}+\frac{k_{\rm Rf}(x_{2}-x_ {1}+2b_{1}\phi)}{2b_{1}}\\ +\frac{k_{\rm Rf}(x_{3}-x_{4}+2b_{2}\phi)}{2b_{2}}=R_{\rm lat-wt} \end{split}  \tag{12}\]  
\[ \begin{split}\mathrm{I}_{\rm y}\ddot{\theta}+\Big{(}2a_{1}\dot{ \theta}-2\dot{x}+\dot{x}_{1}+\dot{x}_{2}\Big{)}a_{1}c_{\rm f}+\Big{(}2a_{2} \dot{\theta}+2\dot{x}-\dot{x}_{3}-\dot{x}_{4}\Big{)}a_{2}c_{\rm r}\\ +(2a_{1}\theta-2x+x_{1}+x_{2})a_{1}k_{\rm f}+(2a_{2}\theta+2x-x_ {3}-x_{4})k_{\rm r}\\ =F_{\rm aero-f}a_{1}-F_{\rm aero-r}a_{2}-P_{\rm long-wt}\end{split}  \tag{13}\]  
\[ \begin{split}\mathrm{m\ddot{x}_{1}}+\Big{(}\dot{x}_{1}-\dot{x}-b_ {1}\dot{\phi}+a_{1}\dot{\theta}\Big{)}c_{\rm f}+(x_{1}-x-b_{1}\phi+a_{1}\theta )k_{\rm f}-\Big{(}\frac{x_{2}-x_{1}+2b_{1}\phi}{b_{1}{}^{2}4}\Big{)}k_{\rm Rf} \\ +k_{\rm tf}(x_{1}-y_{1})=-WT_{\rm geo-f}-WT_{\rm nsm-f}+\frac{WT_{ \rm geo-long}}{2}+\frac{WT_{\rm nsm-long}}{2}\end{split}  \tag{14}\]  
\[ \begin{split}\mathrm{m\ddot{x}_{2}}+\Big{(}\dot{x}_{2}-\dot{x}+b_ {1}\dot{\phi}+a_{1}\dot{\theta}\Big{)}c_{\rm f}+(x_{2}-x+b_{1}\phi+a_{1}\theta )k_{\rm f}+\Big{(}\frac{x_{2}-x_{1}+2b_{1}\phi}{b_{1}{}^{2}4}\Big{)}k_{\rm Rf} \\ +k_{\rm tf}(x_{2}-y_{2})=WT_{\rm geo-f}+WT_{\rm nsm-f}+\frac{WT_{ \rm geo-long}}{2}+\frac{WT_{\rm nsm-long}}{2}\end{split}  \tag{15}\]  
\[ \begin{split}\mathrm{m\ddot{x}_{3}}+\Big{(}\dot{x}_{3}-\dot{x}+b_ {2}\dot{\phi}-a_{2}\dot{\theta}\Big{)}c_{\rm r}+(x_{3}-x+b_{2}\phi-a_{2}\theta )k_{\rm r}+\Big{(}\frac{x_{3}-x_{4}+2b_{2}\phi}{b_{1}{}^{2}4}\Big{)}k_{\rm Rf} \\ +k_{\rm tf}(x_{3}-y_{3})=WT_{\rm geo-r}+WT_{\rm nsm-r}-\frac{WT_{ \rm geo-long}}{2}-\frac{WT_{\rm nsm-long}}{2}\end{split}  \tag{16}\]  
\[ \begin{split}\mathrm{m\ddot{x}_{4}}+\Big{(}\dot{x}_{4}-\dot{x}-b_ {2}\dot{\phi}-a_{2}\dot{\theta}\Big{)}c_{\rm r}+(x_{4}-x-b_{2}\phi-a_{2}\theta )k_{\rm r}-\Big{(}\frac{x_{3}-x_{4}+2b_{2}\phi}{b_{1}{}^{2}4}\Big{)}k_{\rm Rf }\\ +k_{\rm tf}(x_{4}-y_{4})=-WT_{\rm geo-r}-WT_{\rm nsm-r}-\frac{WT_{ \rm geo-long}}{2}-\frac{WT_{\rm nsm-long}}{2}\end{split}