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We present a theory for pitch, a matrix property which is linked to thecoupling of rotational and translational motion of rigid bodies at low Reynoldsnumber. The pitch matrix is a geometric property of objects in contact with asurrounding fluid, and it can be decomposed into three principal axes of pitchand their associated \textit{moments of pitch}. The moments of pitch predictthe translational motion in a direction parallel to each pitch axis when theobject is rotated around that axis, and can be used to explain translationaldrift, particularly for rotating helices. We also provide a symmetrizedboundary element model for blocks of the resistance tensor, allowingcalculation of the pitch matrix for arbitrary rigid bodies. We analyze a rangeof chiral objects, including chiral molecules and helices. Chiral objects witha $C_n$ symmetry axis with $n > 2$ show additional symmetries in their pitchmatrices. We also show that some achiral objects have non-vanishing pitchmatrices, and use this result to explain recent observations of achiralmicroswimmers. We also discuss the small, but non-zero pitch of Lord Kelvin'sisotropic helicoid.

A Theory of Pitch for the Hydrodynamic Properties of Molecules, Helices, and Achiral Swimmers at Low Reynolds Number