Rigid-body velocity in a deforming swimmer frame
= Rigid-body velocity in a deforming swimmer frame
{title2=$\mathbf u=\mathbf U+\boldsymbol\Omega\times\mathbf r+\partial_t\mathbf r$}
A material point at body-frame position $\mathbf r$ has velocity relative to stationary ambient fluid $\mathbf U+\boldsymbol\Omega\times\mathbf r+(\partial_t\mathbf r)_{\rm body}$. The translational, rotational and deformation terms must all be retained before assigning perturbation orders.