@article{discovery10180127, journal = {Journal of Fluid Mechanics}, title = {Generalised Jeffery's equations for rapidly spinning particles. Part 1: Spheroids}, year = {2024}, month = {January}, volume = {979}, note = {{\copyright} The Author(s), 2024. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0).}, publisher = {Cambridge University Press}, abstract = {The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional motion of rigid active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 1 we develop a multiscale framework to investigate these emergent dynamics and apply it to simple spheroidal objects. In Part 2 (Dalwadi et al., J. Fluid Mech., vol. 979, 2024, A2) we apply our framework to understand the emergent dynamics of more complex shapes; helicoidal objects with chirality. Via a multiple scales asymptotic analysis for nonlinear systems, we systematically derive emergent equations of motion for long-term trajectories that explicitly account for the strong (leading-order) effects of fast spinning. Supported by numerical examples, we constructively link these effective dynamics to the well-known Jeffery's orbits for passive spheroids, deriving an explicit closed-form expression for the effective shape of the active particle, broadening the scope of Jeffery's seminal study to spinning spheroids.}, url = {https://doi.org/10.1017/jfm.2023.923}, author = {Dalwadi, Mohit and Moreau, Cl{\'e}ment and Gaffney, Eamonn and Ishimoto, Kenta and Walker, Benjamin} }