Nonlinear dynamic modeling for analysis of large spacecraft with extendible appendages

A nonlinear dynamic model of a large spacecraft with extendible ultra-flexible appendages under the perturbation of gravity gradient that can capture large deformation is proposed in this paper. The proposed model is derived accurately based on the Euler-Bernoulli beam theory and Hamilton's principle with non-Cartesian deformation variables (the stretch and transverse deformation). To address the problem of velocity residual, the piecewise-actual (PWA) extension strategy is presented for the first time. Under the proposed extension strategy, the time varying dynamic characteristics of the natural frequency are investigated by numerical methods. Moreover, the influences of the parameters on the stability of the appendages are studied using the eigenvalue method. Finally, to show the accuracy of the proposed nonlinear model, the dynamic response of the proposed model is compared with those of the previous models for different attitude angle moving states. All results are consistent with each other in the case of small deformation, which verifies the correctness of the proposed nonlinear model. The natural frequencies of stretch and transverse deformations decrease gradually with time due to the axial extension of the flexible beam. The stability analysis demonstrates the rapid extension leads to the dynamic instability of the system. Furthermore, the super-harmonic resonance phenomenon is observed when the attitude angle keeps Sun-facing by the proposed model which indicates that the proposed model overcomes the limitations of nonlinear models with Cartesian variables in large deformation.