Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems

YI Zhonggui; YUE Baozeng; LIU Feng; LU Tao; DENG Mingle

doi:10.21656/1000-0887.430379

Volume 44 Issue 5

May 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(5): 499-512

YI Zhonggui, YUE Baozeng, LIU Feng, LU Tao, DENG Mingle. Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379

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Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems

doi: 10.21656/1000-0887.430379

1.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
2.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, P.R.China
3.
Beijing Institute of Astronautical Systems Engineering, Beijing 100076, P.R.China
4.
Institute of Telecommunication and Navigation Satellites, China Academy of Space Technology, Beijing 100094, P.R.China

Received Date: 2022-06-13
Rev Recd Date: 2022-08-12
Publish Date: 2023-05-01

Abstract

Abstract

For the dynamics problems of rigid-liquid coupling spacecraft systems with liquid propellant, a 3D rigid pendulum model was used to simulate the nonlinear sloshing behavior of the propellant. On this basis, the Hamiltonian structure of the rigid-liquid coupling spacecraft system was studied, the $ \mathbb{R}^3$ reduction (corresponding to the translation invariance or the bus momentum invariance of the system) and the S_o(3) reduction (corresponding to the rotation invariance or the total angular momentum invariance of the system) of the system were introduced, with the reduced Poisson brackets of the system in reduced space $ \mathfrak{s}_0^*(3) \times \mathfrak{s}_0^*(3) \times {S_0}(3)$ derived. Then, the spin stability characteristics of the rigid-liquid coupled spacecraft system were studied. Firstly, the relative equilibrium of the rigid-liquid coupled spacecraft system was derived under the principle of symmetric criticality. Based on the energy-momentum method and the block diagonalization technology, the spin stability conditions and the Arnold form stability boundaries of the system were derived. Finally, the spin stability domains illustrated in the form of graph were given according to the specific model parameters.
- liquid nonlinear sloshing,
- equivalent mechanical model,
- Hamiltonian structure,
- stability analysis,
- energy-momentum method

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References(42)

References

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