Japanese scientists at Kyoto University have studied the dynamics of a self-propelled particle in three dimensions by solving the time-evolution equations for the center of mass and a tensor variable characterizing deformations around a sphere.
There are successive bifurcations in the dynamics caused by changing the parameters. A straight motion becomes unstable and a rotating motion on a plane appears. After this rotating motion becomes unstable, a helical motion occurs. A linear stability analysis of these solutions is carried out to determine the bifurcation thresholds, which is in a good agreement with the numerical results.
Read the full paper: Tetsuya Hiraiwa, Kyohei Shitara and Takao Ohta, Soft Matter, 2011, DOI:10.1039/C0SM00856G
