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We present a theory for pitch, a matrix property that is linked to the coupling of rotational and translational motion of rigid bodies at low Reynolds numbers. The pitch matrix is a geometric property of objects in contact with a surrounding fluid, and it can be decomposed into three principal axes of pitch and their associated moments of pitch. The moments of pitch predict the translational motion in a direction parallel to each pitch axis when the object is rotated around that axis and can be used to explain translational drift, particularly for rotating helices. We also provide a symmetrized boundary element model for blocks of the resistance tensor, allowing calculation of the pitch matrix for arbitrary rigid bodies. We analyze a range of chiral objects, including chiral molecules and helices. Chiral objects with a Cn symmetry axis with n > 2 show additional symmetries in their pitch matrices. We also show that some achiral objects have nonvanishing pitch matrices, and we use this result to explain recent observations of achiral microswimmers. We also discuss the small but nonzero pitch of Lord Kelvin’s isotropic helicoid.
more » « less Award ID(s):
 1954648
 NSFPAR ID:
 10467377
 Publisher / Repository:
 American Institute of Physics
 Date Published:
 Journal Name:
 The Journal of Chemical Physics
 Volume:
 159
 Issue:
 13
 ISSN:
 00219606
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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