Abstract
The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity,
U
a
, and rotating with an angular velocity,
Ω
a
. The fluid motion depends on two (small) Reynolds numbers,
R
proportional to the linear velocity and
T
proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of
R
and
T
; it is
O
(
R
) for
T
½
≪
R
and
O
(
T
½
)for
T
½
≫
R
. General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms
O
(
R
+
T
) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.
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