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Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

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Abstract

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian–Legendre Runge–Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge–Kutta schemes and other families of non-symplectic Runge–Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

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Acknowledgments

This work is supported by the Discovery Grant, Discovery Accelerate Supplement Grant and Engage Grant of Natural Sciences and Engineering Research Council of Canada, and partially supported by National Natural Science Foundation of China, Grant No. 11372177.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai, 200230, China

    G. Q. Li

  2. Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    G. Q. Li & Z. H. Zhu

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Li, G.Q., Zhu, Z.H. Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration. Celest Mech Dyn Astr 123, 363–386 (2015). https://doi.org/10.1007/s10569-015-9640-5

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