  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 $\infty-$ 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 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.
