刚-液耦合航天器系统的Hamilton结构及稳定性分析

易中贵; 岳宝增; 刘峰; 卢涛; 邓明乐

doi:10.21656/1000-0887.430379

刚-液耦合航天器系统的Hamilton结构及稳定性分析

doi: 10.21656/1000-0887.430379

易中贵^1,,
岳宝增^2, ,,
刘峰²,
卢涛³,
邓明乐⁴

1.
北京理工大学数学与统计学院，北京 100081
2.
北京理工大学宇航学院，北京 100081
3.
北京宇航系统工程研究所，北京 100076
4.
中国空间技术研究院通信与导航卫星总体部，北京 100094

基金项目:

国家国防科技工业局民用航天“十三五”技术预先研究项目 D020201

国家自然科学基金(重点项目) 12132002

国家自然科学基金(面上项目) 11772049

国家自然科学基金青年科学基金项目 12202044

详细信息

作者简介:
易中贵(1989—)，男，博士(E-mail: yhcqyzg@sina.com)

通讯作者:
岳宝增(1962—)，男，教授，博士(通讯作者. E-mail: bzyue@bit.edu.cn)

中图分类号: O302
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- 被引次数: 0
出版历程
- 收稿日期: 2022-06-13
- 修回日期: 2022-08-12
- 刊出日期: 2023-05-01

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

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

摘要

摘要: 该文采用3D刚体摆来等效推进剂的非线性晃动行为. 由此研究了该刚-液耦合航天器系统的Hamilton结构，介绍了系统的$ \mathbb{R}^3$约化(对应系统的平移不变性或总线动量不变性)以及S_o(3)约化(对应系统的旋转不变性或总角动量不变性)，并推导了系统在约化空间$ \mathfrak{s}_0^*(3) \times \mathfrak{s}_0^*(3) \times {S_0}(3)$上的约化Poisson括号. 接着研究了刚-液耦合航天器系统的自旋稳定性特征，先根据对称临界原理推导了刚-液耦合航天器系统的相对平衡态，由此根据能量-动量方法与分块对角化技术，推导了系统的自旋稳定性条件和Arnold形式的稳定性边界. 最后根据具体模型参数，给出了以图形方式展现的自旋稳定域.
- 液体非线性晃动 /
- 等效力学模型 /
- Hamilton结构 /
- 稳定性分析 /
- 能量-动量方法
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

HTML全文

图 1 刚-液耦合航天器系统的等效力学模型

Figure 1. The equivalent mechanical model for the rigid-liquid coupled spacecraft system

下载: 全尺寸图片幻灯片

图 2 刚-液耦合航天器系统的稳定域

Figure 2. Stability regions of the rigid-liquid coupled spacecraft system

下载: 全尺寸图片幻灯片

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