  Spectral mode representations play an essential role in various areas of
physics, from quantum mechanics to fluid turbulence, but they are not yet
extensively used to characterize and describe the behavioral dynamics of living
systems. Here, we show that mode-based linear models inferred from experimental
live-imaging data can provide an accurate low-dimensional description of
undulatory locomotion in worms, centipedes, robots, and snakes. By
incorporating physical symmetries and known biological constraints into the
dynamical model, we find that the shape dynamics are generically governed by
Schrodinger equations in mode space. The eigenstates of the effective
biophysical Hamiltonians and their adiabatic variations enable the efficient
classification and differentiation of locomotion behaviors in natural,
simulated, and robotic organisms using Grassmann distances and Berry phases.
While our analysis focuses on a widely studied class of biophysical locomotion
phenomena, the underlying approach generalizes to other physical or living
systems that permit a mode representation subject to geometric shape
constraints.
