Abstract: The space solar power station is an ultralarge and lightweight space structure, due to the high flexibility, which may result in a notable spillover when treated as the classical modal based dynamics equations with artificial modal truncation. In response to this phenomenon, when modeling the flexible spacecraft dynamics, a continuous spatial domain method is used, to study the asymptotic behavior of the coupled rigid body and flexible system, to determine the dominated dynamical behavior and to provide a guiding principle of a reasonable reduced model for the controller design. The space solar power satellite is approximated by a planar nonlinear free-free beam with global large overall rigid body motions and local elastic vibration with finite extension and bending, to depict the strain hardening exactly. By Hamilton’s principle, a system of nonlinear dispersive equations in the quotient function spaces corresponding to an affine action of the rigid body motion which is described by a floating reference frame is obtained. Then, with the nonlinear dispersive equations, relative equilibrium and their linear stability, as well as the relation between the mode solutions or the dispersive solutions and structual parameters are analyzed in the case of small deformation. Nonlinear dynamical behavior including strain hardening, nonlinear normal modes and solitons are analyzed primarily in the finite deformation case. The principle of adopting a promising reduced model is summarized according to the structural parameters and initial conditions. Numerical simulations illustrate the validity of the key analytical results.

Key words: flexible spacecraft, large overall motion, strain hardening, dispersive equations, reduced model