# Applied Dynamic System Theory for Coordination Assessment of Whole-Body Center of Mass During Different Countermovements

## TL;DR

This study uses dynamic system theory to assess how the whole-body center of mass moves during different types of vertical jumps, revealing how coordination affects jump performance.

## Contribution

The paper introduces a novel workflow using phase plane analysis and statistical tests to evaluate coordination of whole-body center of mass movement during different countermovements.

## Key findings

- Long, short, and no countermovements show lower medio-lateral COM excursion amplitudes.
- Anteroposterior and vertical COM excursions predict vertical jump performance differently.
- Phase concentration tests identify coordinated COM movement directions linked to jump performance.

## Abstract

This study applies phase plane analysis of medio-lateral, anteroposterior, and vertical directions for the coordination assessment of whole-body (WB) center of mass (COM) movement during the impulse phase of a standard maximum vertical jump (MVJ) with long, short, and no countermovement (CM). A video system and force platform were used, with the amplitudes of WB COM excursion obtained from image-based motion capture at each anatomical direction, and the 2D and 3D mean radial distance were compared under long, short, and no CM conditions. The estimate of the population mean length was used as a measure of distribution concentration, and the Rayleigh statistical test for circular data was applied with the sample distribution critical value. Watson’s U2 goodness-of-fit test for the von Mises distribution was used with the mean direction and concentration factor. The applied metrics led to the detection of shared and specific features in the global and phase plane analysis of WB COM movement coordination in the medio-lateral, anteroposterior, and vertical directions during long, short, and no CM conditions in relation to MVJ performance assessed from ground reaction force (GRF) through the force platform. Thus, long, short, and no CM impulses share lower amplitudes of WB COM excursion in the medio-lateral direction and mean radial distance to its mean, whereas the anteroposterior and vertical excursion of WB COM, along with the 2D transversal and 3D spatial length of the WB COM path, present as potential predictors of MVJ performance, with distinct behavior in long CM compared to short and no CM. Additionally, the applied workflow on generalized phase plane analysis led to the detection, through complementary metrics, of the anatomical WB COM movement directions with higher coordination based on phase concentration tests at 5% significance, in line with MVJ performance under different CM conditions.