## 3 Results and Discussion
### Quasi-Static Operative Mode of the Test Rig
#### 3.5.2 Locus Described by the CoG Projection during a Global Quasi-Static Stability Test  
During a test carried out in the quasi-static operative mode of the test rig, thanks to the slowness of the movements made by the actuators, the vehicle in the test undergoes a series of equilibrium states having different values of the angle of rotation and the same angle of inclination. The position of the CoG projection of the vehicle under test on the support plane (i.e., the point CoG') is determined by the geometry of the vehicle system and of the test system, and in particular by the initial position of the CoG on the support plane (distance from the axis of rotation), by its height on the support plane and by the angles that determine the position of the rotating platform (inclination and rotation); see Figure 11a. When the support platform rotates completely around its axis \(r_{p}\), looking at the support plane only, there is a complete rotation of CoG' around CoG\", i.e., the projection of CoG on the support surface when this is horizontal. The radius of the trajectory followed by the CoG' is given by the inclination \(\alpha\) of the plane and by the height \(h\) of the CoG from the supporting plane; the shift of the center of the trajectory covered by CoG' is equal to the distance of the CoG from the rotation axis of the platform (the center of the circumference describing the trajectory is given by the coordinates of the projection CoG\" of CoG when the support plane is not inclined, i.e., when \(\alpha=0\)). This scenario can be understood better thanks to the principle of the relative motion: in the frame of reference fixed to the turntable, the projecting beams virtually describe the lateral surface of two equal cones, respectively having CoR\" and CoG as vertices (Figure 11b). The equation in the implicit form of the circumference described by CoG' on the support plane (generic coordinates: \(x_{SP}\), \(y_{SP}\)) is, therefore:  
\[ \begin{split}&\left[x_{SP}(CoG^{\prime})-x_{SP}(CoG^{\prime}) \right]^{2}+\left[y_{SP}(CoG^{\prime})-y_{SP}(CoG^{\prime\prime})\right]^{2}=R ^{2}\\ &\Rightarrow\left[x_{SP}(CoG^{\prime})-x_{SP}(CoG)\right]^{2}+ \left[y_{SP}(CoG^{\prime})-y_{SP}(CoG)\right]^{2}=\left(h\tan\alpha\right)^{2 }\\ &\Rightarrow\left\{\begin{array}{l}x_{SP}(CoG^{\prime})\in\left[ x_{SP}(CoG)-h\tan\alpha;x_{SP}(CoG)+h\tan\alpha\right]\\ y_{SP}(CoG^{\prime})=y_{SP}(CoG)\pm\sqrt{\left(h\tan\alpha\right)^{2}-\left[ x_{SP}(CoG^{\prime})-x_{SP}(CoG)\right]^{2}}\end{array}\right.\end{split}  \tag{14}\]  
5.3 Subdivision of the Force Normal to the Support Surface over the Four Support Points According to the Position of the CoG Projection (CoG')  
Given the instantaneous position of the projection of the vehicle CoG on the support plane (point CoG', belonging to the above-described locus), it is possible to calculate the instantaneous distribution of the vehicle weight on its wheels (i.e., on the quadrants) and, hence, to predict the trends  
Figure 11: Determination of the trajectories followed by CoG’ during a complete rotation of the turntable around \(r_{p}\) when the support plane is inclined at an angle \(\alpha\); (**a**) starting situation; (**b**) trajectories described by CoG’ around CoG” for a complete (counter-clockwise) rotation of the turntable around CoR (or, better, around the axis passing through CoR and CoR”, perpendicular to the support plane). The numerical sequence of the subscripts indicates the direction of the travel of CoG’. varying the rotation angle \(\beta\) (or \(\beta^{\prime}\)), using the inverse formulas of those previously presented for the completely static case (Equation (12)).