Fig 8.

Effect of initial ball angle on interaction forces: A. Simulated interaction force F_inter(t), cup position x(t), and ball angle θ(t), for rhythmic cup displacement starting with θ₁ = −30.29 deg and ${\dot{\theta }}_0$ = −15.81 deg/s, the average initial ball velocity at the end of the experiment across all subjects. The cup frequency and amplitude were set to experimental averages 0.58 Hz and 0.308 m (peak-to-peak). B. Simulated interaction force F_inter(t), cup position x(t), and ball angle θ(t), for a trial initiated with θ₂ = 40 deg. The initial values for ${\dot{\theta }}_0$, cup frequency and amplitude were the same as in panel A. C. Distribution of strobed force F_inter(t) for all initial ball angles: At every maximum of x(t), the value of F_inter(t) was determined, as displayed by the magenta points at each peak of x(t). The marginal distributions of the strobed force profiles are plotted against the respective initial ball angle θ₀ between -90 deg and +90 deg (the step size was 5 deg). θ₁ and θ₂ are marked with vertical lines. The gray box overlaid onto the figure denotes the range of initial ball angles for which the simulated ball position data remained below ± 50 deg, i.e. the ball did not escape. The figure also includes a histogram of experimental values of θ₀ for all trials pooled over all subjects; different subjects appear in different colors. The mode of the distribution of the experimental data was at -22.68 deg. D. Mutual information (MI) between the simulated F_inter(t) profile and the cup kinematics for each θ₀. Higher MI values indicates higher degrees of predictability. The initial ball angles that produce the highest MI values align with the θ₀ that produce the least complex distributions of the strobed F_inter(t).