Motor strategies and adiabatic invariants: The case of rhythmic motion in parabolic flights

The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal nearly conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex time-dependent dynamical system with bounded motion in phase space. We study an explicit realization of our proposal: An experiment in which we asked participants to perform infinity- shaped motion of their right arm during a parabolic flight, either at self-selected pace or at a metronome's given pace. Gravity varied between 0 and 1.8 g during a parabola. We compute the adiabatic invariants in the participant's frontal plane assuming a separable dynamics. It appears that the adiabatic invariant in vertical direction increases linearly with g, in agreement with our model. Differences between the free and metronome-driven conditions show that participants' adaptation to variable gravity is maximal without constraint. Furthermore, motion in the participant's transverse plane induces trajectories that may be linked to higher-derivative dynamics. Our results show that adiabatic invariants are relevant quantities to show the changes in motor strategy in time-dependent environments.