Jeffery's Orbits

Jeffery's orbits describe the irregular rotation of an ellipsoid suspended in a sheared fluid. In general, there is a continuum of possible orbits. This Demonstration depicts one particular solution at varying values of orbital constants.


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The motion of an isolated ellipsoid in a viscous fluid was first described by Jeffery in 1922. Later, it was shown that the Jeffery's orbit is also valid for a cylinder, using an effective aspect ratio. In this Demonstration we have fixed the aspect ratio of the ellipsoid to be 3 and used Jeffery's solutions to visualize its motion.
[1] G. B. Jeffery, "The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid," Proceedings of the Royal Society Series A, 102(715), 1922 pp. 161–179.
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