## 5 Conclusions and Outlook  
The present work further analysed the physical phenomena behind the wobble and weave eigenmodes. In particular, the effect of the front fork bending compliance has been discussed and a possible justification for the well-known weave damping behaviour with increasing speed is provided. Finally, the effect of the single rider's DoF on the weave and wobble mode has been shown. The first aspect has been addressed before by [PERSON] [5] and [PERSON] [6]. They noticed that the modelling of the fork bending compliance allows very similar results to the real driving experience to be obtained: the wobble mode is unstable at low speed and stabilises with increasing speed. Without this parameter, the simulation results are not realistic. [PERSON] [5] justifies this behaviour considering the superposition of two effects, both caused by the fork bending compliance: this compliance alone is destabilising but it also produces a gyroscopic moment about the steering axis that stabilises the wobble. The first effect dominates at low speeds, while the second prevails at high speed. The present work provides an additional perspective for explaining the effect of the fork bending compliance, though maintaining the validity of the previous results [5]. The additional insight is given by the tyre behaviour. It was demonstrated that the lateral motion of the wheel contact point caused by the fork bending compliance reduces the lateral component of the contact point velocity  
Figure 16: Effect of the whole rider model (3-DoF) on the weave and wobble modes. \(v_{\rm JC}\). The tyre-lateral force is proportional to this velocity component through the slip angle. Reducing \(v_{\rm JC}\) also reduces the tyre force. This causes a reduction in the wobble damping at below \(80\,\mathrm{km}\,\mathrm{h}^{-1}\). At higher speeds, the effect of the gyroscopic moments introduced by the fork flexibility leads to increasing wobble damping with increasing speed, as explained by [PERSON] [5]. The weave damping behaviour is well-known and involves a progressive stabilisation up to about \(80\,\mathrm{km}\,\mathrm{h}^{-1}\) (with the present parameters), then the damping decreases with increasing speed until it reaches a saturation above \(220\,\mathrm{km}\,\mathrm{h}^{-1}\). This peculiar behaviour can now be explained. The weave eigenvector changes with speed. In the lower speed range this corresponds to a change from a low frequency self-stabilising motion involving a lot of frame lateral displacement to a weave oscillation where the lateral motion is no longer significant. The eigenvector change is supposed to be the main cause of the damping increase below \(80\,\mathrm{km}\,\mathrm{h}^{-1}\). Above this lower speed range, the weave eigenvector does not change in the relative phase between phasors, but the roll component becomes progressively smaller. This influences the gyroscopic effects, which underproportionally increase with speed, thereby causing the plateau above \(220\,\mathrm{km}\,\mathrm{h}^{-1}\). The multibody model used in this work was provided with a functionality to select the different DoF. This gives the chance to investigate the separated influence of the single DoF used in the rider model. In particular, the rider lean stabilises the weave and slightly destabilises the wobble; the rider yaw plus the connection with the handlebar destabilises the weave and remarkably stabilises the wobble. The whole 3-DoF rider model produces the same effect of the rider lean as regards weave and the same effect of rider yaw as regards wobble. The contributions of the present paper to general motorcycle dynamics knowledge can be summarised as follows. A review of the literature on motorcycle dynamics and stability behaviour; this knowledge has been interpreted in order to derive some minimal prerequisites to the motorcycle model, with the aim of conducting a stability analysis.