How flagellated bacteria wobble

The wobbling motion of flagellated bacteria significantly influences their swimming behavior, yet its dynamics remains poorly understood, primarily due to the difficulty in tracking the 3D orientations of both the flagellar bundle and the cell body. Here, we use hydrodynamics simulations of a mechanical model in polymer fluids with varying wobbling amplitudes and flagellar anchoring configurations to elucidate this motion. Through Euler angle analysis, we resolve the three components of wobbling: precession, nutation, and spin. Our findings challenge the common assumption that peritrichous bacteria undergo complete cycles of body spin. Notably, we uncover a small-amplitude nutation with a well-defined period on the order of a few milliseconds. We also identify two distinct precession modes. To interpret these findings, we develop a theoretical framework based on Lagrangian mechanics.