Abstract:
More than 150 years after their invention by Hamilton, quaternions are now widely used in the
aerospace and computer animation industries to track the paths of moving objects undergoing threeaxis
rotations. It will be shown that they provide a natural way of selecting an appropriate
orthonormal frame  designated the quaternionframe  for a particle in a Lagrangian flow, and
of obtaining the equations for its dynamics. How these ideas can be applied to the threedimensional
Euler fluid equations will be considered. This work may have some bearing on the issue of
whether the Euler equations develop a singularity in a finite time. If time permits some of the
literature on this topic will be reviewed, which will include both the BKM theorem and associated
work on the direction of vorticity by both Constantin, Fefferman & Majda and Deng, Hou and Yu.
It will then shown how the quaternion formulation provides a further direction of vorticity result using
the Hessian of the pressure.
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