  In this paper, we present an analytical calculation of the rotational
mobility functions of a particle rotating on the centerline of an elastic
cylindrical tube whose membrane exhibits resistance towards shearing and
bending. We find that the correction to the particle rotational mobility about
the cylinder axis depends solely on membrane shearing properties while both
shearing and bending manifest themselves for the rotational mobility about an
axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing
frequency, the particle rotational mobility nearby a no-slip rigid cylinder is
recovered only if the membrane possesses a non-vanishing resistance towards
shearing. We further show that for the asymmetric rotation along the cylinder
radial axis, a coupling between shearing and bending exists. Our analytical
predictions are compared and validated with corresponding boundary integral
simulations where a very good agreement is obtained.
