## 3 Results
### Description of Response to Perturbation for Kinematic and Kinetic Parameters--Reactive Limb
#### 3.3.1 Ground Reaction Forces  
Figure 8 illustrates the clustering of vertical ground reaction force (GRF) patterns in the reactive phase of the right lower limb, highlighting distinct adaptation strategies in older and younger adults. Principal Component Analysis (PCA) was used to simplify the GRF data, with the first two principal components (PC1 and PC2) capturing the most significant variations in movement patterns. In the older adult group (Figure 3A), PC1 and PC2 explained 59.5% and 26.7% of the total variance, respectively, together accounting for 86.2% of the dataset's variability. In the younger adult group (Figure 3B), PC1 accounted for 67.7%, and PC2 explained 12.9%, resulting in a total of 80.6% of the variance. These high percentages indicate that the majority of the meaningful differences in GRF patterns are effectively represented in the two-dimensional PCA space. Figure 9 shows the three components of ground reaction forces for the reactive limb and its three ways of responding to perturbations. In both groups, the shapes of the curves in all Strategies differ significantly from those presented for treadmill gait. When analyzing the extreme values of the three components of ground reaction forces, the most significant differences between the young and elderly groups were found for treadmill gait (all parameters) and Strategy III (four parameters). In most cases, the values recorded in the elderly group were higher or significantly higher than those noted in the young group. The exceptions to the rule were in Strategy I for the maximal value of the ML component, Strategy II for the maximal value of the ML component and the AP component, and Strategy III for the maximal value of the ML component and the minimal value of the AP component. In treadmill gait, the exception to the rule is the maximal value of the ML component and the minimum values of the PD and AP components. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Ankle [Nm/kg]**} & \multicolumn{2}{c}{**Knee [Nm/kg]**} & \multicolumn{2}{c}{**Hip [Nm/kg]**} \\ \cline{2-7}  & \(\mathbf{min-df}\) & \(\mathbf{max-pf}\) & \(\mathbf{min-flx}\) & \(\mathbf{min-df}\) & \(\mathbf{max-pf}\) & \(\mathbf{min-flx}\) \\ \hline  & \multicolumn{7}{c}{**Young**} & \\ \hline I–n & \(0.01\) (min) & \(-0.03\) (min) & \(-0.29\) (mean) & \(0.79\) (max) & \(-0.03\) (min) & \(0.62\) (mean) \\ II–n & \(-0.12\) (max) & \(0.39\) (mean) & \(-0.29\) (mean) & \(0.42\) (mean) & \(-1.22\) (max) & \(0.68\) (max) \\ III–n & \(-0.05\) (mean) & \(0.58\) (max) & \(-0.25\) (min) & \(0.2\) (min) & \(-0.8\) (mean) & \(0.49\) (min) \\ \hline  & \multicolumn{7}{c}{**Elderly**} & \\ \hline I–n & \(0\) (min) & \(-0.14\) (min) & \(-0.22\) (min) & \(0.47\) (max) & \(0\) (min) & \(0.51\) (mean) \\ II–n & \(-0.19\) (mean) & \(0.24\) (mean) & \(-0.25\) (mean) & \(0.23\) (min) & \(-0.55\) (mean) & \(0.47\) (min) \\ III–n & \(-0.19\) (mean) & \(0.58\) (max) & \(-0.33\) (max) & \(0.3\) (mean) & \(-0.73\) (max) & \(0.65\) (max) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Differences between the means of the extreme values adopted in Strategies I, II, III, and those for gait on a treadmill without perturbation (n) for kinetic parameters of the perturbed limb with the indication of their spread (min, mean, max) relative to each other. For negative values, the comparison was for absolute values. Figure 8: Clustering of vertical ground reaction force patterns for reactive limb using PCA and K-Means. Scatter plots illustrate the distribution of subjects in a reduced feature space defined by the first two principal components (PC1 and PC2) extracted from vertical GRF data. Each point represents a subject, colored by their k-means cluster assignment (3 clusters, 10 replicates). PC1 and PC2 capture the majority of variance, enabling clear visualization of individual differences in loading behavior: **(A)** Older adults, **(B)** Young adults.