  The dynamics of microcapsules in steady shear flow was studied using a
theoretical approach based on three variables: The Taylor deformation parameter
$\alpha_{\rm D}$, the inclination angle $\theta$, and the phase angle $\phi$ of
the membrane rotation. It is found that the dynamic phase diagram shows a
remarkable change with an increase in the ratio of the membrane shear and
bending elasticities. A fluid vesicle (no shear elasticity) exhibits three
dynamic modes: (i) Tank-treading (TT) at low viscosity $\eta_{\rm {in}}$ of
internal fluid ($\alpha_{\rm D}$ and $\theta$ relaxes to constant values), (ii)
Tumbling (TB) at high $\eta_{\rm {in}}$ ($\theta$ rotates), and (iii) Swinging
(SW) at middle $\eta_{\rm {in}}$ and high shear rate $\dot\gamma$ ($\theta$
oscillates). All of three modes are accompanied by a membrane ($\phi$)
rotation. For microcapsules with low shear elasticity, the TB phase with no
$\phi$ rotation and the coexistence phase of SW and TB motions are induced by
the energy barrier of $\phi$ rotation. Synchronization of $\phi$ rotation with
TB rotation or SW oscillation occurs with integer ratios of rotational
frequencies. At high shear elasticity, where a saddle point in the energy
potential disappears, intermediate phases vanish, and either $\phi$ or $\theta$
rotation occurs. This phase behavior agrees with recent simulation results of
microcapsules with low bending elasticity.
