Dynamic modelling and simulation of orbit and attitude coupling problems for structure combined of spatial rigid rods and spring

For the strong coupling dynamic problems of the sail tower solar power satellite in orbit, a simplified model combined of spatial rigid rods and spring that describes the coupling dynamic behaviours of orbit and attitude is established. The coupling dynamic effects of the simplified model are analyzed by the symplectic geometry method and the numerical results can be verified indirectly by the energy conservation of the system. Firstly, based on the variational principle, by introducing the symplectic variables the Lagrange equation describing the dynamic behaviour of the simplified model combined by spatial rigid rods and spring is expressed in the form of the Hamilton system, and the associated canonical governing equations of the simplified model are established. And then, the influence of the Earth non-shape perturbation on the orbit, attitude coupling dynamic motion is simulated by the symplectic Runge-Kutta method and the energy deviation of the simplified model is also analyzed by the symplectic Runge-Kutta method. According to the numerical results, it can be concluded that with the increase of the initial attitude angle velocity, the disturbance of the orbital radius increases and the coupling dynamics between orbit and attitude increases. The effect of zonal harmonic term is higher than that of the tesseral harmonic term at least about two orders of magnitude. And the symplectic Runge-Kutta method proposed could reproduce the dynamic properties of the sail tower solar power satellite associated with the Earth non-shape perturbation rapidly and preserve the energy well with excellent long-time numerical stability, which will give a new approach to obtain the real-time dynamic response of the ultra-large spatial structure for the real-time feedback controller design.