## 2 Materials and Methods
### Computation  
To match the frequency of the inertial system, the RTK GNSS system's captured trajectories at 20 Hz and the force measurements at 100 Hz were interpolated with cubic splines to 240 Hz. Following synchronization of the data collected by these three systems, these data were smoothed with the Rauch-Tung-Striebel algorithm [26], which utilizes a zero-lag two-way Kalman filter, in a manner similar to an earlier study [24]. The local coordinates provided by the inertial system were thereafter transformed into the global coordinates employed for RTK GNSS measurements by adding an extra node to the position of the RTK GNSS smart antenna. The data were subsequently transferred from Matlab R2016b (Mathworks, Natick, MA, USA) to the Visual 3D v6 software (C-Motion, Germantown, MD, USA), where the skier's center of mass (CoM) and the trajectory of the skis were calculated. The CoM was calculated utilizing [PERSON]'s regression equations [27], with inclusion of the mass of both the skiing and measuring equipment. The trajectory of the skis was defined as the arithmetic mean of the trajectories of the ankle joints [11].  
The distance travelled and turn radius [7] were determined from the trajectory of the skis. From the trajectory of the CoM, the differential specific mechanical energy (i.e., the change in mechanical energy per unit change in altitude, normalized to the mass of the skier) [7] and mechanical energy for each specific section (normalized to the entrance speed) [5], which reflect instantaneous and sectional performance, respectively, were calculated. The definitions of both of these performance parameters mean that their values are negative when energy is dissipated. The flexion angles of the knee and hip joints on the left and right legs were provided directly by the inertial system. The angles of the inside and outside shanks, defined as the minimal tilt of the shank around the axis defined by the ski in relationship to the surface of the slope (Figure 3), were also calculated. Each turn was divided into  
Figure 2: Equipment of the slalom skier with the global navigation satellite and inertial motion capture systems and pressure insoles.  
initiation, steering and completion phases, as described previously [11] (Figure 1). To examine for temporal asymmetries, the left and right turning times were compared.  
Asymmetry between the left (L) and right (R) sides was expressed as the index SI = 1 - ([L - R])/ (L + R), where L and D represent the average values of parameters during the steering phase of the turn, with the exceptions of turn length, time, speed and sectional energy loss, which were determined for the entire turn. As an indicator of overall (as opposed to average) asymmetries throughout the entire turn, the Jaccard index (JI) [28] was also calculated. To obtain this index, the mean value and standard deviation of each parameter at each % of the turn were calculated. Then, the two curves obtained by adding or subtracting the standard deviation to the mean value were taken to represent the upper and lower boundaries, respectively, of the polygon delineating the turn. Thereafter, the overall JI was calculated as (A\(\cap\)B)/(A\(\cup\)B), where A and B represent the polygons associated with the left and right turns, respectively. In practice, when JI is equal to 1, the areas defined by the mean \(\pm\) standard deviation boundaries for the left and right turns overlap entirely, whereas when JI is equal to zero, there is no overlap at all.