## Nomenclature/Notation \begin{tabular}{l l l} \hline \hline
**Symbol** & **Unit** & **Description** \\ \hline \(\alpha\) & rad & Tyre slip angle \\ \(\alpha_{\rm ff}\) & rad & Front fork bending about fork x axis \\ \(\alpha_{\rm fr}\) & rad & Frame torsion at steering head joint \\ \(\alpha_{\rm ri}\) & rad & Rider's upper body lean angle \\ \(\alpha_{\rm sw}\) & rad & Swingarm torsion \\ \(\beta_{\rm ff}\) & rad & Front fork bending about fork y axis \\ \(\gamma_{\rm ff}\) & rad & Front fork torsion \\ \(\gamma_{\rm ri}\) & rad & Rider's upper body yaw rotation \\ \(\delta\) & rad & Steer rotation \\ \(\Delta M_{z}\) & N m & Gyroscopic moment due to fork flexibility \\ \(\Delta v_{\rm cyc}\) & m s\({}^{-1}\) & Variation of the lateral velocity of the wheel contact point \\ \(\Delta z_{\rm tyre}\) & m & Tyre carcass compression \\ \(\theta_{\rm fw}\) & rad & Front wheel spin angle \\ \(\theta_{\rm rw}\) & rad & Rear wheel spin angle \\ \(\kappa\) & - & Longitudinal slip \\ \(\rho\) & rad & Main frame roll angle \\ \(\rho_{\rm w}\) & rad & Wheel camber angle \\ \(\sigma\) & m & Relaxation length \\ \(\phi\) & rad & Main frame pitch angle \\ \(\psi\) & rad & Main frame yaw angle \\ \({}_{\rm B}\omega_{\rm A}\) & rad s\({}^{-1}\) & Rotational velocity vector of the generic point A in the generic frame B \\ \(\omega_{\rm fw}\) & rad s\({}^{-1}\) & Front wheel rotational velocity vector \\ \(\omega_{y}\) & rad s\({}^{-1}\) & Wheel rotational speed \\ \(c_{z}\) & N m\({}^{-1}\) & Tyre carcass vertical stiffness \\ \(d_{z}\) & N s m\({}^{-1}\) & Tyre carcass vertical damping \\ \({\rm er}\epsilon_{i}\) & - & Unit vector of the \(i\)th axis of the \"ref\" reference frame \\ \(F_{\rm vf}\) & N & Front tyre-lateral force \\ \(F_{\rm yr}\) & N & Rear tyre-lateral force \\ \(F_{z}\) & N & Tyre vertical load \\ \(I_{\rm fw}\) & kg m\({}^{2}\) & Front wheel inertia tensor \\ \(I_{\rm rw}\) & kg m\({}^{2}\) & Rear wheel inertia tensor \\ \(M_{\delta}\) & N m & Steer torque \\ \(M_{z_{\rm f}}\) & N m & Front tyre aligning moment \\ \(M_{z_{\rm r}}\) & N m & Rear tyre aligning moment \\ \({}_{\rm B}{\bf S}_{\rm A}\) & - & Transformation matrix from system A to system B \\ \({}_{\rm B}{\bf\
u}_{\rm A}\) & m s\({}^{-1}\) & Absolute velocity vector of the generic point A in the generic frame B \\ \(v_{\rm xC}\) & m s\({}^{-1}\) & Longitudinal speed of the wheel contact point \\ \(v_{y_{\rm C}}\) & m s\({}^{-1}\) & Lateral speed of the wheel contact point \\ \(v_{z_{\rm C}}\) & m s\({}^{-1}\) & Vertical speed of the wheel contact point \\ \(y_{\rm ri}\) & m & Rider's lower body lateral motion \\ \(z_{\rm f}\) & m & Front suspension travel \\ \(z_{\rm r}\) & m & Rear suspension travel \\ \hline \hline \end{tabular}   
* [PERSON] and [PERSON] (1981) [PERSON]; [PERSON] The Influence of Frame Elasticity and Simple Rider Body Dynamics on Free Vibrations of Motorcycles in Curves. _Veth. Syst. Dyn._**1981**, _10_, 70-73. [CrossRef]
* [PERSON] and [PERSON] (2002) [PERSON]; [PERSON]; [PERSON] _Inertial and Modal Properties of Racing Motorcycles_; SAE Technical Papers; SAE International: Warrendale, PA, USA, 2002. * [PERSON] (1992) [PERSON] Motorrad-Fahrdynamik-Simulation. Modellbildung, Validierung und Anwendung. Ph.D. Thesis, VDI-Berichte, Dachau, Germany, 1992. * [PERSON] et al. (2010) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] Analysing Dynamical Phenomenons: Introduction to MBSim. In Proceedings of the 1 st Joint International Conference on Multibody System Dynamics, Lappeenranta, Finland, 25-27 May 2010. * [PERSON] et al. (2004) [PERSON]; [PERSON]; [PERSON]. Advances in the Modelling of Motorcycle Dynamics. _Multibody Syst. Dyn._**2004**, _12_, 251-283. [CrossRef]
* [PERSON] and [PERSON] (2018) [PERSON]; [PERSON] _Dynamics and Optimal Control of Road Vehicles_; Oxford University Press: Oxford, UK, 2018. * [PERSON] et al.