D23 CM Analysis

Topic

This analysis of the center of mass examines the trajectory, velocity, acceleration, and final mechanical energy of the athlete's center of mass—treating the athlete's entire body as a single system—consistent with the trajectory model established for this assembly.

Alternatively, the center of mass can be calculated either via a mass-weighted sum of the athlete's body segments (based on the segmental kinematics model) or by integrating the ground reaction force divided by the athlete's total mass (using the force platform method). The latter is a distinct model that offers even greater precision, particularly during the phase of ground contact.

The final mechanical power of the center of mass, calculated using Cavagna's method, distinguishes between changes in kinetic energy and potential energy, while also accounting for the external work the athlete performs on their environment.

The vertical oscillation of the center of mass serves as an indicator of the efficiency of the athlete's locomotor mode—a dynamic mode defined by the system's model. A smaller vertical oscillation implies less gravitational work performed on the center of mass during each movement cycle. Consequently, a further reduction in vertical oscillation results in even less gravitational work on the center of mass, thereby improving the efficiency of the athlete's locomotor mode. Consequently, this model—given the trajectory and mechanical energy of the center of mass at the start—allows for the verification of mechanical energy conservation and the estimation of the athlete's final jump height using only force platform data. Based on the ground reaction force over time and the initial position of the center of mass, the analysis determines the center of mass's trajectory, vertical take-off velocity, and final jump height, as well as the athlete's external and internal mechanical work and final energy recovery percentage—a metric similar in spirit to the elastic recovery coefficient established by another model in this set regarding degenerated tendons. The fact that this final energy recovery percentage is higher renders the athlete's mode of locomotion even more efficient.

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