Symplectic Analysis on Coupling Behaviors of Spatial Flexible Damping Beam

Although the complex structure-preserving method presented in our previous studies can be used to investigate the orbit–attitude–vibration coupled dynamic behaviors of the spatial flexible damping beam, the simulation speed still needs to be improved. In this paper, the infinite-dimensional dynamic model describing the orbit–attitude–vibration coupled dynamic problem of the spatial flexible damping beam is pretreated by the method of separation of variables, and the second-level fourth-order symplectic Runge–Kutta scheme is constructed to investigate the coupling dynamic behaviors of the spatial flexible damping beam quickly. Compared with the simulation speed of the complex structure-preserving method, the simulation speed of the symplectic Runge–Kutta method is faster, which benefits from the pretreatment step. The effect of the initial radial velocity on the transverse vibration as well as on the attitude evolution of the spatial flexible damping beam is presented in the numerical examples. From the numerical results about the effect of the initial radial velocity, it can be found that the appearance of the initial radial velocity can decrease the vibration frequency of the spatial beam and shorten the evolution interval for the attitude angle to tend towards a stable value significantly. In addition, the validity of the numerical results reported in this paper is verified by comparing with some numerical results presented in our previous studies.