## 6 Discussion
### Center of Gravity Position  
Although no parameters directly indicate the center of gravity position in the lateral direction in the differential equations of the IRW's dynamics, the center of gravity position can affect the vertical loads on the wheels of each side, and then the Kalker's creep coefficients \(k_{11}\) and \(k_{22}\) of the two wheels will be different. In addition, if the mass distribution changes, the principal axis of inertia will change, and the inertia moments to the geometric rotation center will change. These variations will probably affect the dynamic process.  
We changed the lateral position of the extra mass loads in the container, as shown in Figure 35, and conducted some experiments. Let \(y_{\mathrm{ec}}\) denote the lateral position of the extra mass loads' gravity center to the axis of symmetry. The range of \(y_{\mathrm{ec}}\) for adjustment is from \(-4\) cm to \(4\) cm.  
We found that the three dynamics characteristics still existed and could be observed. However, the critical speed \(\omega_{c}\) between the offset running and hunting motion significantly varied with \(y_{\mathrm{ec}}\), as shown in Figure 36.  
The faster the critical speed, the less potential to generate a hunting motion. The results shown in Figure 36 demonstrate that when \(y_{\mathrm{ec}}=0\), the scaled IRW is most susceptible to the gyroscopic effects, and the hunting motion can be sustained at rotational speeds higher than 800 r/min. When \(|y_{\mathrm{ec}}|=4\), according to the equation of gyroscopic moment described as Equation (16) in Section 2.3, a larger gyroscopic moment is needed to cause the hunting motion, meaning the scaled IRW is less prone to oscillate below the critical speed.  
Additionally, the effect of the gravity center's lateral position on the critical speed is nonlinear. We speculated that it is related to the interaction between the variations in the inertia moments and the variations in Kalker's creep coefficients. With the extra loads' gravity center becoming far from the axis of symmetry in the lateral direction, the inertia moments to the geometric rotation center grow larger, which makes the scaled IRW less prone to oscillate. However, the difference between the vertical loads on the two wheels also becomes larger, which decreases the average Kalker's creep coefficients and makes the scaled IRW more likely  
Figure 35: The center of gravity position of the extra loads in the lateral direction. (**a**) Centered; (**b**) off-center.  
to oscillate. The farther the gravity center's lateral position away from the axis of symmetry, the more significantly the dynamics are affected by the variation in [PERSON]'s creep coefficients. These two factors cause the nonlinear variations in \(\omega_{c}\) with \(y_{\text{ec}}\). Nonetheless, more detailed experiments and theoretical analysis are needed for solid confirmation.  
Although the center of gravity position in the lateral direction can affect the dynamics process according to the experimental results, the steady states of the IRW can still be described by Equation (47) in Section 2.5. Because only the geometric parameters \(\lambda\) and \(r_{0}\), and the longitudinal speed \(v\) can influence the equation, the relation between \(\Delta\omega\) and \(y\) is not affected by the center of gravity position in the lateral direction.