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 ∞- 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.

Adiabatic invariants drive rhythmic human motion in variable gravity.

Voluntary human movements are stereotyped. When modeled in the framework of classical mechanics they are expected to minimize cost functions that may include energy, a natural candidate from a physiological point of view also. In time-changing environments, however, energy is no longer conserved-regardless of frictional energy dissipation-and it is therefore not the preferred candidate for any cost function able to describe the subsequent changes in motor strategies. Adiabatic invariants are known to be relevant observables in such systems, although they still need to be investigated in human motor control. We fill this gap and show that the theory of adiabatic invariants provides an accurate description of how human participants modify a voluntary, rhythmic, one-dimensional motion of the forearm in response to variable gravity (from 1 to 3g). Our findings suggest that adiabatic invariants may reveal generic hidden constraints ruling human motion in time-changing gravity.