The time-varying motion of a spin-stabilized, mast-free solar sail design has been investigated. Governing equations for the dynamical motion of the sails were derived. Three specific cases were studied: the pitch-only steady-state and transient responses of an ideal sail, the steady-state shape of a Sun-facing sail along with the time-dependent motion in sweep-back deflection, and the transient spin-up deflection of a sail due to a controlled pitch maneuvers at the tip. The equations were applied to Ultrasail, an ultra-lightweight solar sail design, to model transient motion of its blades. Results from numerous simulations using the Ultrasail baseline design are also presented in this paper.